ENERGY/MATTER CONVERSION METHODS AND STRUCTURES

Abstract: Methods and apparatus for releasing energy from hydrogen atoms (molecules) by stimulating their electrons to relax to quantized lower energy levels and smaller radii (smaller semimajor and semiminor axes) than the "ground state" by providing energy sinks or means to remove energy resonant with the hydrogen energy released to stimulate these transitions. An energy sink, energy hole, is provided by the transfer of at least one electron between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one or more donating species to one or more accepting species whereby the sum of the ionization energies and/or electron affinities of the electron donating species minus the sum of the ionization energies and/or electron affinities of the electron accepting species equals approximately m x 27.21 eV (m x 48.6) for atomic (molecular) hydrogen below "ground state" transitions where m and t are integers. The present invention further comprises methods and structures to conform the energies of the source, hydrogen, and the sink, energy hole, to enhance the transition rate. The energy reactor includes one of an electrolytic cell, a pressurized hydrogen gas cell, and a hydrogen gas discharge cell.

Description: ENERGY/MATTER CONVERSION METHODS AND STRUCTURES This application is a continuation-in-part of the co-pending application of Randell Lee Mills, entitled Energy/Matter Conversion Methods and Structures", filed on June 11, 1993, which is a continuation-in-part of the subject matter published June 25,1992 in WO 90/10838 and November 01, 1990 in WO 90/1312,6. BACKGROUND OF THE INVENTION 1. Field of the Invention: This invention relates to methods and apparatus for releasing energy from hydrogen atoms (molecules) as their electrons are stimulated to relax to lower energy levels and smal ler radi i (smal ler semimajor and semiminor axes) than the "ground state" by providing energy sinks or means to remove energy resonant with the electronic energy released to stimulate these transitions according to a novel atomic model. Each of such reactions is hereafter referred to as a shrinkage reaction: each transition is hereafter referred to as a shrinkage transition: each energy sink or means to remove energy resonant with the hydrogen electronic energy released to effect each transition is hereafter referred to as an energy hole, and the electronic energy removed by the energy hole to effect or stimulate the shrinkage transition is hereafter referred to as the resonance shrinkage energy. The present invention further comprises methods and structures for repeating this shrinkage reaction to produce shrunken atoms (molecules) to provide new materials with novel properties such as high thermal stabi lity. 2. Description of the Related Art As a result of the erroneous assumptions and incomplete or erroneous models and theories, the development of useful or functional systems and structures requiring an accurate understanding of atomic structure and energy transfer has been inhibited The Schrodinger equation, for example, does not explain the phenomenon of anomalous heat release from hydrogen in certain electrolytic cells having a potassium carbonate electrolyte with the production of lower-energy hydrogen atoms and molecules, which is part of the present invention Thus, advances in materials and energy/matter conversion have been largely limited to laboratory discoveries having limited or sub-optimal commercial application. SUMMARY OF THE INVENTION A novel atomic theory is disclosed in The Unification of Spacetime. the Forces. Matter, and Energy. Mills, R, Technomics Publishing Company, Lancaster, PA. U.S.A. (1992); The Grand Unified Theory. Mills. R. and Farrell, J. , Science Press, Ephrata, PA (1990); Mills, R. , Kneizys, S. , Fusion Technology, 210, (1991) ,pp 65-81, and in my previous U.S. patent applications entitled: "Energy /Matter Conversion Methods and Structures." whose subject matter was published June 25, 1992 in WO 90/10838 and November 01, 1990 in WO 90/13126. The present invention comprises methods and apparatuses for releasing heat energy from hydrogen atoms (molecules) by stimulating their electrons to relax to quantized potential energy levels below that of the "ground state " via electron transfer reactions of reactants including electrochemical reactant(s) (electrocatalytic couple(s)) which remove energy from the hydrogen atoms (molecules) to stimulate these transitions In addition, this application includes methods and apparatuses to enhance the power output by enhancing the reaction rate- the rate of the formation of the lower-energy hydrogen The present invention further comprises methods and apparatuses for repeating a shrinkage reaction according to the present invention to cause energy release and to provide shrunken atoms and molecules with novel properties such as high thermal stability, and low reactivity The lower-energy state atoms and molecules are usef ul for heat tran- cryogeni c appl icati ons, as a buoyant gas, as a medium i n an eng ine - as a Sterl ing engine or a turbine , as a general replacement for hel ium and as a refr igerant by absorbing energy includi ng heat energv as the electrons are exc ited back to a h igher energy l evel Below " Ground State " Transit ions of Hydrogen Atoms According to a novel model of the electron derived from f i rst principles (Uni f ication of Spaceti me. the Forces. Matter, and Energv. Mil ls, R., Technomics Publishing Company, Lancaster, PA, ( 1 992)), bound electrons are described by a charge-density (mass-density) function which is the product of a radial delta function (f(r) = δ(r-r n )), two angular functions (spherical harmonic functions), and a time harmonic function. Thus, an electron is a spinning, two-dimensional spherical surface, cal l ed an electron orbitsphere, that can exist in a bound state at only specif ied distances from the nucleus where each point on the shell fol lows a great circle orbit about the central nucleus. For the "ground state", the electric field is a radial central f ield inside the spherical shell and zero outside, where the radius of the shell is the Bohr radius, a 0 . At this radius, the electron is nonradiative, and a force balance exists between the central field of the proton and the electron. Photon Induced States of the One Electron Atom Excited states of hydrogen arise from the capture of a photon(s) of discrete resonant frequencies. The bound electron can trap photons of discrete frequencies inside this spherical shel l, a spherical resonator cavity. For the exci ted modes, the electric field is the sum of the "ground state" field and a time harmonic solution of the Laplacian in spherical coordinates. The electric field is nonzero inside of an expanded resonator cavity where the radius at which nonradiation and force balance is achieved is an integer multiple of the Bohr radius The photons which exc ite these modes have energy n f > nj For a spherical resonator cavity, the relationship between an allowed radius, r, and the photon standing wave wavelength, λ, is 2πr = nλ (2) where n is an integer The relationship between an allowed radius and the electron wavelength is 2π(nr 1 ) = 2τrr n = nλ< = λ n (3) where n = 1 n = 2, 3, A, ... _ 1 1 1 n 2 ' 3 ' 4 ' •■ λi is the allowed wavelength for n = 1 n is the allowed radius for n = 1 Higher and lower energy states are equally valid. The photon standing wave in both cases is given as a solution of the Laplacian in spherical coordinates. Excited State Photon (A) For n = 2, 3, A, ... i = 1, 2, ..., n - 1 m = -I, -Si * 1, ..., 0, ..., +J. Below "Ground State" Photon εir photon n,l.m (φ,θ) + Y m s s ] ] (5) For n = 2, 3, 4, ... 1 = 1, 2, ..., n - 1 m = -i, -i. + 1, ..., 0, ..., +1 According to Eq (5). the magnitude of the central field corresponding to below " ground state " transitions is an integer, and the energy of below " ground state " transitions are given by n f < n, From energy conservation, the resonance energy hole of a hydrogen atom a 0 which exci tes resonator modes of radial dimensions r is m + 1 m x 27 2 e , ( where m = 1 , 2, 3, 4, After resonant absorption of the hole, the radius of the orbitsphere, a 0 , shrinks to — — and after p cycles of resonant shrinkage, the radius a 0 ιs mp + 1 • In other words, the radial "ground state" field can be considered a the superposition of Fourier components The removal of negative Fourier components of energy m x 27.2 eV, where m is an integer increases the positive electric field inside the spherical shel l by m times the charge of a proton. The resultant electric field is a time harmonic solution of the Laplacian in spherical coordinates In this cas the radius at which force balance and nonradiation are achieved is do + . where m is an integer. In decaying to this radius from the " ground state", a total energy of [(m + I ) 2 - 1 2 3 x 13.6 eV is released. The total energy well of the hydrogen atom is shown in FIGURE 1. The exothermic reaction involving transitions from one potential energy level to a lower level is hereafter referred to as HECTER (Hydrogen Emission by Catalytic Thermal Electronic Relaxation). A hydrogen atom with its electron in a lower than "ground state" energy level corresponding to a fractional quantum number is hereafter referred to as a hydπno atom The designation for a hydrino atom of a 0 " a • Ό radius — where p is an integer is H The size of the electron orbitsphere as a function of potential energy is given in FIGURE 2 Energy Hole (Atomic Hydrogen) In a preferred embodiment, energy holes, each of approximately 27 21 eV, are provided by electron transfer react ions of reactants including electrochemical reactant(s) (electrocatalytic couple(s)) which cause heat to be released from hydrogen atoms as their electrons are stimulated to relax to quant ized potential energy leve ls below that of the "ground state" The energy removed by an electron transfer reaction, energy hole, is resonant with the hydrogen energy released to stimulate this transition The source of hydrogen atoms is the production on the surface of a cathode during electrolysis of water in the case of an electrolytic energy reactor and hydrogen gas or a hydride in the case of pressurized gas energy reactor or gas discharge energy reactor. Below "Ground State" Transitions of Hvdrogen-Tvpe Molecules and Molecular Ions Two hydrogen atoms react to form a diatomic molecule, the hydrogen molecule. 2 H[a 0 ] - H 2 [2C = β a 0 ] (8 where 2c" is the internuclear distance. Also, two hydrino atoms react to form a diatomic m where p is an integer. The central force equation for hydrogen-type molecules has orbital solutions which are circular, ell iptic, parabolic, or hyperbolic. The former two types of solutions are associated with atomic and molecular orbitals. These solutions are nonradiative if the boundary condition for nonradiation given in the One Electron Atom Section of The Unification of Spacetime. the Forces. Matter, and Energy. Mills, R., Technomics Publishing Company, Lancaster, PA, ( 1992), is met. The mathematical formulation for zero radiation is that the function that describes the motion of the electron must not possess space-time Fourier components that are synchronous with waves travell ing at the speed of light. The boundary condition for the orbitsphere is met when the angular frequencies are As demonstrated in the One Electron Atom Section of The Unif icat ion of Spacetime. the Forces. Matter, and Energy. Mi l ls, R , Technomics Publ ishing Company, Lancaster, PA, ( 1992), this condition is met for the product funct ion of a radial Dirac delta function and a t ime harmonic 7 function where the angular frequency, ω, is constant and given by Eq ( 10) TΓL iϊ m e where L is the angular momentum and A is the area of the closed geodesic orbit Consider the sol ution of the central force equation comprising the product of a two dimensional ell ipsoid and a time harmonic function. The spatial part of the product function is the convolution of a radial Dirac delta function with the equation of an ellipsoid. The Fourier transform of the convolution of two functions is the product of the individual Fourier transforms of the functions; thus, the boundary condition is met for an ellipsoidal-time harmonic function when _ rfi_ h ωn = m e A = m e ab ( 1 2 where the area of an ellipse is A = τrab ( 13 where 2b is the length of the semiminor axis and 2a is the length of the semimajor axis. The geometry of molecular hydrogen is elliptic with the internuclear axis as the principle axis; thus, the electron orbital is a two dimensional el lipsoidal-time harmonic function. The mass follows geodesies time harmonically as determined by the central field of the protons at the foci. Rotational symmetry about the internuclear axis further determines that the orbital is a prolate spheroid. In general, ell ipsoidal orbits of molecular bonding, hereafter referred to as ell ipsoidal molecular orbitals (M. 0. 's), have the general equation The semiprinciple axes of the ell ipsoid are a, b, c. In el l ipsoidal coordinates, the Laplacian is δ δφ δ δψ δ δφ < π - )R ξ δ ( R ξ δ ) - < ϊ - O^ - ^ - ) ♦ U - *( ( - ) - ° < ' 5> An ell ipsoidal M 0 is equivalent to a charged conductor whose surface is given by Eq ( 14) It carries a total charge q, and it ' s potent ial is a solution of the Laplacian in ellipsoidal coordinates, Eq ( 15) Excited states of orbi tspheres are discussed in the Excited States of the One Electron Atom (Quantization) Section of The Unif ication of Spacetime. the Forces, Matter, and Energy. Mills, R , Technomics Publishing Company, Lancaster, PA, ( 1 92) In the case of el l ipsoidal l 5 0 's, excited electronic states are created when photons of discrete frequencies are trapped in the el lipsoidal resonator cavity of the M 0 The photon changes the ef fective charge at the Ii. 0. surface where the central field is ellipsoidal Force balance is achieved at a series of ellipsoidal equipotential two dimensional surfaces confocal with the 0 ground state ellipsoid. The trapped photons are solutions of the Laplacian in ellipsoidal coordinates, Eq ( 15). As is the case with the orbitsphere, higher and lower energy state are equally valid. The photon standing wave in both cases is a solution of the Laplacian in ellipsoidal coordinates. For an ellipsoidal resonator 5 cavity, the relationship between an allowed circumference, 4aE, and the photon standing wavelength, λ, is 4aE = nλ (.16 where n is an integer and where a2 - b2 k = ^— ( 17 0 is used in the ell iptic integral E of Eq. ( 16). Applying Eqs. ( 16) and ( 17), the relationship between an allowed angular frequency given by Eq. ( 12) and the photon standing wave angular frequency, ω, is: πh " h tL_ _ _L m e A " mena^b] ~ m e a n b n ~ n 2 ωι ~ ωn where n = 1 , 2, 3, 4, ... R . 1 1 1 O n 2 ' 3 ' 4 ' - ωi is the allowed angular frequency for n = 1 3 \ and b] are the allowed semimajor and semiminor axes for n = 1 From Eq ( 18), the magnitude of the el liptic field corresponding to a 0 below " ground state " transition of the hydrogen molecule is an integer The potent here ^o a = (2 1 and where p is an integer. From energy conservation, the resonance energy hole of a hydrogen-type molecule which causes the transition 2 a 0 ao H *2 2c " = *2 2C = ? (24 m i s mp 2 X 48.6 eV (25 where m and p are integers. During the transition, the ell iptic field is increased from magnitude p to magnitude p + m. The corresponding potential energy change equals the energy absorbed by the energy hole. Energy hole = -V e - V p = mp 2 X 48.6 eV (26 Further energy is released by the hydrogen-type molecule as the internuclear distance "shrinks". The total energy, ET, released during th transition is ( m + -pp)H 2 VV22]1.. V V22Z + 1 Eτ = - 13.6 eV 2( m + p) 2 V2 - ( m + p) 2 V2 - ( m + p) 2 V2 yβ - + 13.6 eV (zp f - p* 5 A ψ} n A schematic drawing of the total energy well of hydrogen-type molecules and molecular ions is given in FI GURE 3. The exothermic reaction involving transitions from one potential energy level to a lower level below the " ground state " is also hereafter referred to as HECTER (Hydrogen Emission by £atalytic Thermal Electronic Re laxation). A hydrogen-type molecule with its electrons in a lower than " ground state " energy level corresponding to a fractional quantum number is hereafter referred to as a dihydπno molecule ' The designat ion for a dihydri no molecule of internuclear di stance, 2c ' = where p is an P 9873 0 integer, is H*2J zc = 5 ao i schematic drawinq of the size of hydrogen-type molecules as a function of total energy is given in F IGUR 4 The magnitude of the el l ipt ic f ield correspondi ng to the f irst belo "ground state " hydrogen-type molecule is 2 From energy conservation, the resonance energy hole of a hydrogen molecule which excites the transition of the hydrogen molecule with internuclear distance 2c ' -. V ao to the first below " ground state " with internuclear distance 2C = ao is given by Eqs. ( 19) and (20) where the elliptic field is increased from magnitude one to magnitude two: -2e2 a a2 - p V e = In = -67.813 eV (2 δπεcn/ a 2 - b 2 '" a - J a 2 - b 2 e Vn = , = 1 .23 eV (2 δπεo- a 2 _ 2 Energy hole = -V e - V p = 48.6 eV (3 In other words, the ellipsoidal "ground state" field of the hydrogen molecule can be considered as the superposition of Fourier components. The removal of negative Fourier components of energy m x 48.6 eV (3 ] where m is an integer, increases the positive electric field inside the ell ipsoidal shell by m times the charge of a proton at each focus. The resultant electric field is a time harmonic solution of the Laplacian in ell ipsoidal coordinates. The hydrogen molecule with internuclear distance 2c " = yf~2 ao is caused to undergo a transition to a below " ground state" level, and the internuclear distance for which force balance and nonradiat ion are achieved is 2c ' = . In decaying to this internuclear distance from the " ground state " , a total energy of ( 1 + m ) 2 V2 is released Energy Hole (Molecular Hvdroαen) In a preferred embodiment, energy holes, each of approximately m X 48 6 eV, are provided by electron transfer reactions of reactants including electrochemical reactant(s) (electrocatalytic couple(s)) which cause heat to be released from hydrogen molecules as their electrons are stimulated to relax to quantized potential energy leve ls below that of the "ground state". The energy removed by an electron transfer reaction, energy hole, is resonant with the hydrogen energy released to stimulate this transition. The source of hydrogen molecules is the production on the surface of a cathode during electrolysis of water in the case of an electrolytic energy reactor and hydrogen gas or a hydride in the case of a pressurized gas energy reactor or gas discharge energy reactor. Energy Reactor The present invention of an electrolytic cell energy reactor, pressurized gas energy reactor, and a gas discharge energy reactor, comprises: a means for containing a source of hydrogen; a means for bringing the hydrogen atoms (molecules) into contact with one of a solid, molten, liquid, or gaseous solution of energy holes; and a means for removing the lower-energy hydrogen atoms (molecules) so as to prevent an exothermic shrinkage reaction from coming to equilibrium. The shrinkage reaction rate and net power output can be increased by conforming the energy hole to match the resonance shrinkage energy. In general, power output is optimized by controll ing the temperature, pressure of the hydrogen gas, the source of the energy hole including the electrocatalytic couple which provides the energy hole, the counterion of the electrocatalytic couple, and the area of the surface on which the shrinkage reaction occurs. In the case of an electrolytic cell , power output is opt imized by controll ing the the electric field of the electrolysis cell as a function of time, the pH of the solution, the surface area of the cathode, the current density of the cathode, and the material composition and structure of the cathode In the case of atomic hydrogen shrinkage, further enhancement of the 'electrolytic cel l can be achieved by preventing the development of a hydrogen gas boundary layer between the surface of the cathode where the reacting hydrogen atoms 9873 12 are generated and the sol ut ion which contains the e lectrocatalytic couple This can be achieved by applyi ng vibration or ul trasound to the cathode and /or electrolyti c solution and by the use of an elec trolysis circuit where the current is intermittent Other objects, features, and characterist ics of the present invention, as wel l as the methods of operation and the funct ions of the related elements, wi l l become apparent upon considerat ion of the fol lowing description and the appended claims with reference to the accompanying drawings, al l of which form a part of this specification, wherein l ike reference numerals designate corresponding parts in the various figures. BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 is a schematic drawing of the total energy wel l of the hydrogen atom; FIGURE 2 is a schematic drawing of the size of electron orbitspheres as a function of potential energy; FIGURE 3 is a schematic drawing of the total energy wel ls of the hydrogen molecule, H2 2c' = 2 a 0 J, the hydrogen molecular ion, H2[2c' = 2a 0 ] , the dihydπ ' no molecule, H*2| 2c ' = = , and the dihydrino molecular ion, + H* 2 [2C = a 0 ] ; FIGURE 4 is a schematic drawing of the size of hydrogen-type molecules, H* as a function of total energy; 2C' FIGURE 5 is a schematic drawing of an energy reactor in accordance with the invention, FIGURE 6 is a schematic drawing of an electrolytic cel l energy reacto in accordance wi th the present invention; FIGURE 7 is a schemat ic drawing of a pressurized gas energy reactor in accordance wi th the present invent ion, FIGURE 8 is a schemat ic drawing of a gas discharge energy reactor in accordance wi th the invention, F I GURE 9 i s the experi menta l calorimeter set-up 1 - vacuum jackete dewar, 2 - thermistor, 3 - Pt anode, 4 - Ni cathode, 5 - magnetic stirrin bar, 6 - resistor heater, 7 - rubber stopper, 8 - Tef l on tubing, 9 - magneti c stirrer, 1 0 - a lumi nium cy l inder, FIGURE 1 0 is the Experiment - 1 pl ot of the heat ing coeff icients versus tune 1 - electrolysis with a nickel wire cathode at 0 083 A in K2CO3, 2 - resistor working in K2CO3, FIGURE 1 1 is the Experiment *2 plot of the heating coeff icients versus time. 1 - electrolysis with a nickel cathode and a periodic square-wave having an offset voltage of 1.60 volts; a peak voltage of 1.90 volts; a peak constant current of 47.3 mA; a 36.0% duty cycle; and a frequency of 600 Hz in K2CO3, 2 - resistor working in K2CO3; FIGURE 1 2 is the Experiment *3 plot of the heating coeff icients versus time. 1 - electrolysis at 0.081 A in Na2C03, 2 - resistor working in Na2 03; FIGURE 13 is the ESCA analysis of a control nickel sheet; FIGURE 1 A- 14D are the ESCA analysis of a sample of the nickel cathode from each of an aqueous potassium carbonate electrolytic cell and a control aqueous sodium carbonate electrolytic cel l; FIGURE 15 is a schematic of the cryofiltration apparatus; and FIGURE 16 is a plot of the intensity verses ionization potential of the mass spectroscopic analysis of cryofi ltered electrolysis gases evolved from the potassium electrolytic cell. TABLE 1 is the power input and output parameters of Experiment * 1 - *3; TABLE 2 is the Faradaic efficiency of gas production by the heat producing K2CO3 cell and Na2C03 control cel l; TABLE 3 is the observed extreme ultraviolet background emission dat of interstellar space [Labov, S., Bowyer, S., "Spectral observations of the extreme ultraviolet background " , The Astrophysical Journal , 37 1 , ( 1 991 ), pp 81 0-819] according to Eq. (3 1 4), TABLE 4 is the binding energies of the hydπno atom as a function of principle quantum number according to Eq (31 2), TABLE 5 is data of the mass spectroscopic analysis with varying ionization potential of standard hydrogen, TABLE 6 is data of the mass spectroscopic analysis with varying ionization potential of cryof i ltered standard hydrogen, TABLE 7 is data of the mass spectroscopic analysis with varying ionizat ion potent ia l of gases from the cryof i lter alone, TABLE 8 is data of the mass spectroscopic analysis wi th varying ion izat ion potent ial of cryof i ltered electrolysis gases evo lved from the sodium electrolytic cel l; and TABLE 9 is data of the mass spectroscopic analysis with varying ionization potential of cryof iltered electrolysis gases evolved from the potassium electrolytic cell. DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS THEORY Below "Ground State" Transitions of Hydrogen Atoms For the hydrogen atom, the radius of the " ground state" orbitsphere is a 0 . This orbitsphere contains no photonic waves and the centripetal force and the electric force balance is a 0 4πε 0 a 0 2 where v-i is the velocity of the electron in the " ground state " , and m e is the electron mass. It was shown in the Excited States of the One Electron Atom (Quantization) Section of Unification of Soacetime. the Forces. Matter, and Energy. Mills, R., Technomics Publ ishing Company, Lancaster, PA, ( 1992) that the electron orbitsphere is a resonator cavity which can trap electromagnetic radiation of discrete frequencies. The photon electric field functions are solutions of the Laplacian in spherical coordinates. The photons decrease the nuclear charge to 1 /n and increase the radius of- the orbitsphere to na 0 The new configuration is also in force balance rn e n 2 e 2 /n XX ~ = — ; ? ( 4) na 0 4πε 0 (na 0 K where v n is the velocity in the nth excited state corresponding to radius r n = na 0 For a spherical resonator cavity, the nonradiative boundary condition and the relationship between an al lowed radius and the photon standing wave wavelength. Eq (2), gives rise to Eq (3), the boundary condition for allowed radi i and al lowed electron wavelengths as a function of the parameter n Each value of n corresponds to an allowed transit ion effected by a resonant photon which excites the transiti on in the orbitsphere resonator cavity I addition to the traditional integer values ( 1 , 2, 3, ,), n values of fractions are allowed by Eq (3) which correspond to transitions with an increase in the nuclear charge and decrease in the radius of the orbitsphere. This occurs, for example, when the orbitsphere couples to another resonator cavity which can absorb energy. This is the absorption of an energy hole The absorption of an energy hole destroys the balance between the centrifugal force and the increased central electric force As a result, the electron undergoes a transition to a lower energy nonradiative state. For the He + ion (Z = 2; a one-electron atom) an allowed state exists at 0.5 a 0 . It can be shown that if a "ground state" hvdroαen atom emits a photon of about 27.21 eV, the photonic wave in the orbitsphere creates an effective charge at the orbitsphere such that the electron experiences an effective charge of +2e, and establishes a new centripetal/electric equilibrium at r</2 = 0.5 a 0 . That is, the orbitsphere shrinks from n = a 0 7 0 f f p2 2 X 2 Θ 2 V = - — — = - — = - 4 x 27.1 78 eV = - 108.70 eV (35) 4πε 0 r 1 2 4πε 0 a 0 The kinetic energy of the shrunken orbitsphere is - V, or T = 54.35 eV. The "ground state" hydrogen atom has a net energy of - 13.59 eV and the final hydrogen atom has a net energy of -5442 eV (same as He + ), and ΔE = -40.83 eV for the reaction H(Z β ff = 1 ; n = a 0 ) → H(Z eff = 2; r 1 /2 = 0 5 a 0 ) . (36) That is, about 27.21 eV is lost with the absorption of the energy hole and about 14 eV is given off after absorption of the energy hole From energy conservation, the resonance energy hole of a hydrogen atom which excites resonator modes of radial dimensions m x 27 2 eV, (37) where m = 1 , 2, 3, 4, After resonant absorpti on of the hole, the radius of the orbitsphere, a 0 , a 0 shrinks to -— . and after p cycles of resonant shrinkage, the radius . a o mp + 1 I n other words, the radial " ground state " field can be considered as the superpositi on of Fouri er components The remova l of negative Fourier components of energy m x 27.2 eV, where m i s an integer increases the positive electric field inside the spherical shel l by m times the charge of a proton. The resultant electric field is a time harmonic solution of Laplace ' s equations in spherical coordinates. I n this case, the radius at which force balance and nonradiation are an achieved is + . where m is an integer. In decaying to this radius from the "ground state", a total energy of [(m + I ) 2 - I 2 ] x 13.6 eV is released. The process is hereafter referred to as HECTER (Hydrogen Emission by Catalytic Thermal Electronic Relaxation). ENERGY HOLES The same energy hole can continue the shrinkage cycle. In general, absorption of an energy hole wil l cause the orbitsphere to undergo a transition from one stable non-radiative radius to another stable non- radiative radius. The electric force is attractive, thus, the orbitsphere wil l shrink when the effective nuclear charge increases. The orbitsphere has an initial radius, r n , initial effective nuclear charge, Z e ff , and initial velocity, v n , given by the condition for non-radiation ( 39 ) At force balance, m e (r n )3 4πε 0 (r n ) 2 ( 40 ) Shrinkage occurs because the effective nuclear charge increases by an integer, m, when Eqs ( 38-40 ) are satisfied by the introduction of an energy sink of a coupled resonator, such as an electron orb itsphere resonator cavity comprising an electrochem ical coupl e or other electron transfer reaction The coupled resonator provides energy holes and affects the shrinkage transition from the initial radius a 0 /(mp+l) and a nuclear charge of (mp + i ' to tne second radius , + , — ~ and a nuclear charge of m(p+1) + 1 Energy conservation and the boundary condition that trapped photons must be a solution to the Laplacian i spherical coordinates determine that the energy hole to cause a shrinkage is given by Eq. (37). As a result of coupling, the hydrogen atom emits a photon of m x 27.21 eV, and this photon is absorbed by the coupled resonator. Stated another way, the hydrogen atom absorbs an energy hole of m x 27.21 eV. The energy hole absorption causes a second photon to be trapped in the hydrogen atom electron orbitsphere. Recall from the Excited States of the One Electron Atom (Quantization) Section of Mills, R., Unification of Spacetime. the Forces. Matter, and Energy. Technomics Publishing Company, Lancaster, PA, (1992) that electromagnetic radiation of discrete energy can be trapped in a resonator cavity. As shown previously, the photonic equation must be a solution of the Laplacian in spherical coordinates. The photon field comprises an electric field which provides force balance and a nonradiative orbitsphere. The solution to this boundary value problem of the radial photon electric field is given by <V ,m m s εtr photon n.l,m ■ = ^ X. ( -1 ♦ n [ Y 0 ( .Θ) Y ]] (41) For n = 2, 3, 4, ... 1 = 1, 2, .... n - 1 m = -1, -1 + 1, ..., 0, ..., +1 And, the quantum numbers of the electron are n, 1, m (m^), and m s . It is apparent from this equation that given an initial radius of and a final radius of that the nuclear charge . (mp 1) m(p + 1) + is increased by m with the absorption of an energy hole of m x 27.2 eV. The potential energy decreases by this energy, thus, energy is conserved However, the force balance equation is not initially satisfied as the effective nuclear charge increases by m Further energy is emitted as 1 8 force balance is achieved at the final radius By replacing the initial radius with the final radius, and by increasing the charge by m in Eq (40) r , -,-κ f |2 r M ( ( m ( ρ + D + De)e m ( p- 1 ) + I P — 7-3 = m ( p* l ) + \ )V " — ~ - — ~ , (42 rrie o 4πε 0 a c force balance is achieved and the orbitsphere is non-radiative The energy balance for m = 1 is as fol lows An initial energy of 27.2 1 eV is emitted as the energy hole absorption event. This increases the effective nuclear charge by one and decreases the potential by 27.2 1 eV. More energy is emitted until the total energy released is [(p + 1 ) 2 - p 2 ] x 13.6 eV where p is an integer. Several examples of different energy holes effecting shrinkage and the corresponding effective nuclear charges, total energy released, and final radii of the orbitspheres going from infinity to the final radius, a 0 /(m + 1 ) are given in the fol lowing table. Radii, energies, energy holes, and energy released for several states of hydrogen. Energy released for any transition is given by ΔEf jn'al (∞ to R) - ΔEjni tial (00 to R) CATALYTIC ENERGY HOLE STRUCTURES FOR ATOMS Single Electron Transfer An energy hole is pn-i.'ided b> the transfer of an electron between participating species including atoms, ions, molecules, and ionic and molecular compounds In one embodiment, the energy hole comprises the transfer of an electron from one species to another species whereby the sum of the ionization energy of the electron donating species m inus the ionization energy or electron affinity of the electron accepting species equals approximately m X 27.21 eV where m is an integer. Single Electron Transfer (Two Species) An efficient catalytic system that hinges on the coupling of three resonator cavities involves potassium. For example, the second ionization energy of potassium is 31.63 eV. This energy hole is obviously too high for resonant absorption. However, K + releases 4.34 eV when it is reduced to K. The combination of K + to K 2+ and K + to K, then, has a net energy change of 27.28 eV; m = 1 in Eq. (37). 27.28 eV + K + + K + + H ^ 1 - K + K 2+ + J ( 8 + ° ^ + [(p + 1 ) 2 - p 2 ] x 13.6 eV (43) K + K + - K + + K + + 27.28 eV (44) And, the overall reaction is H[ j → H[ (p ° t ) ] + [(p + 1 ) 2 -p 2 ] x 13.6 e V (45) Note that the energy given off as the atom shrinks is much greater than the energy lost to the energy hole And, the energy released is large compared to conventional chemical reactions. For sodium or sodium ions no electrocatalytic reaction of approximately 27 21 eV is possible For example, 42 15 eV of energy is absorbed by the reverse of the reaction given in Eq (44) where Na + replaces K + Na + + Na + + 42 15 eV → Na - Na 2 + (46) Other less efficient catalytic systems that hinge on the coupl ing of three resonator cavities exist For example, the third ionizat ion energy of palladium is 32 93 eV This energy hole is obviously too high for resonant absorption However, Lι + releases 5 392 eV when it is reduced to Li The combination of Pd 2+ to Pd 3+ and Lι + to Li, then, has a net energy change of 27.54 eV. 275 eV + Lι + + Prj 2+ + H| ~ — ~ \→ Ll + P 3+ + H TT " ^ 2- f ~ + [(p + 1 ) 2 - p 2 ] x 136 eV (47) Li + Pd 3+ = Lι + + Pd 2+ + 2754eV (48) And, the overall reaction is H + [( P + 1)2 - p 2] x 13.6 eV (49) Single Electron Transfer (One Species) An energy hole is provided by the ionization of an electron from a participating species including an atom, an ion, a molecule, and an ionic or molecular compound to a vacuum energy level. In one embodiment, the energy hole comprises the ionization of an electron from one species to a vacuum energy level whereby the ionization energy of the electron donating species equals approximately m X 27.21 eV where m is an integer. Titanium is one of the catalysts that can cause resonant shrinkage because the third ionization energy is 27.49 eV, m = 1 in Eq. (37). Thus, the shrinkage cascade for the p th cycle is represented by 27.491 eV + Ti 2+ + Hp ~\→ Ti3 + + e ~ + H τ ~ T) 1 + t(p + D 2 - p 2 ] x 13.6 eV (50) Ti3 + + e- - Ti2 + + 27.491 eV (51) And, the overall reaction is H H [(p+ I) 2 -p ' 2] x 13.6 eV (52) |_(p + 1) Rubidium(l) is also a catalyst. The second ionization energy is 27.28 eV. 27.28 eV+ Rb + + fi 1 - Rb 2+ + e " + J. °° ] 1 + [(p + 1 ) 2 - p 2 ] x 13.6eV (53) Rb 2+ + e ~ - Rb + + 27.28 eV (54) And, the overall reaction is 2 H . H I(p ÷ I) 2 -p2] ' x 13.6 eV (55) LP (P + 1) J Other single electron transfer react ions to provide energy holes of approximately mi X 27.21 eV where m is an integer appear in my previous U.S Patent Applications ent itled " Energy/ Matter Conversion Methods and Structures," fi led on December 12, 1990 and April 28, 1 989, which are incorporated herein by ref erence Multiple Electron Transfer An energy hole is provided by the transfer of multiple electrons between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one or more species whereby the sum of the ionization energies and/or electron affinities of the electron donating species minus the sum of the ionization energies and/or electron affinities of the electron acceptor species equals approximately m X 27.21 eV where m and t are integers. An energy hole is provided by the transfer of multiple electrons between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one species to another whereby the t consecutive electron affinities and/or ionization energies of the electron donating species minus the t consecutive ionization energies and/or electron affinities of the electron acceptor equals approximately m X 27.21 eV where m and t are integers. In a preferred embodiment the electron acceptor species is an oxide such as Mn0χ, A10χ, SiOχ. A preferred molecular electron acceptor is oxygen, 02- Two Electron Transfer(One Species) In an embodiment, a catalytic system that provides an energy hole hinges on the ionization of two electrons from an atom, ion, or molecule to a vacuum energy level such that the sum of two ionization energies is approximately 27 21 eV Zinc is one of the catalysts that can cause resonant shrinkage because the sum of the first and second ionization energies is 27 358 eV, m = 1 in Eq (37) Thus, the shrinkage cascade for the p th cycle is represented by 22 27 358 eV + Zn + H ( 56 Zn2 + + 2e " n 27 358 eV (57 And, the overal l reaction is H [(p + I ) 2 -p2] x 13 6 eV (58 I P (p + i ) Catalytic systems that hinge on the transfer of two electrons from an atom to a vacuum energy level capable of producing energy holes for shrinking hydrogen atoms are given in the following table. The sum of th first ionization energy, IE ι , plus the second ionization energy, IE2, equals approximately 27.21 eV. As an example, Zn + 27.358 eV = Zn 2+ + 2e ~ where IE i + IE2 equals 27.358 eV. In another embodiment, a catalytic system that provides an energy hole hinges on the transfer of two electrons from an atom, ion, or molecule to another atom or molecule such that the sum of two ionizati on energies m inus the sum of two electron affinities of the participating atoms, ions, and/or molecules is approximately 27.21 eV. A catalytic system that hinges on the transfer of two electrons from an atom to a molecule involves palladium and oxygen For example, the first and second ionization energies of pal ladium are 8 34 eV and 1 9 43 eV, respectively And, the first and second electron aff ini ties of the oxygen molecule are 0 45 eV and O i l eV, respective ly The energy hole resulting from a two electron transfer is appropriate for resonant absorption The combinat ion of Pd to Pd 2 + and O2 to 02 ~ , then, has a net energy change of 27 21 eV O 94/29873 23 27 21 eV + P + 0? + H - Pd 2 + 0' .2- f ( p + 1 )2 _ p 2j x 1 3 P J L( P + 0 eV (5 Pd Pd + 0 2 + 27 2 1 eV (6 And, the overa reaction is " a Ό, a n Hi H [(p + 1 )2 -p2] x 13.6 eV (6 P J UP + i ) Additional atoms, molecules, or compounds which could be substituted for O2 are those with first and second electron affinities of approximately 0.45 eV and 0. 1 1 eV, respectively, such as a mixed oxide 10 (MnOχ, A10χ, SiO x ) containing 0 to form 0 2" or 0 2 to form 0 2 2~ . Catalytic systems which could be substituted for Pd in Eqs. (59-61 ) tha hinge on the transfer of two electrons from an atom to oxygen or to an atom, ion, or molecule with first and second electron affinities of approximately 0.45 eV and 0. 1 1 eV, respectively, that are capable of 1 5 producing energy holes for shrinking hydrogen atoms are given in the following table. 20 25 In another embodiment, a catalytic system that provides an energ hole hinges on the transfer of two electrons from an atom, ion, or molecule to another atom, ion, or molecule such that the sum of two 30 ionization energies minus the sum of one ionization energy and one electron affini ty of the participating atoms, ions, and/or molecules is approximately 27 21 eV A catalytic system that hinges on the transfer of two electrons from an atom to an ion involves xenon and lithium. For example, the first and second ionizat ion energies of xenon are 12. 1 3 eV " ^ and 21 21 eV, respectively And, the f irst ionizat ion energy and the firs electron affinity of lithium are 539 and 062 eV, respectively The energy hole resulting from a two electron transfer is appropriate for resonant absorption The combination of Xe to Xe 2+ and Lι + to Lr, then, has a net energy change of 2733 eV 2733eV + Xe + L ' eV Xe2 + + Li " Xe Lι And, the overall reaction is H - H ϊ(p+ I) -p2] x 13.6 eV (64) (P + 1) J Catalytic systems that hinge on the transfer of two electrons from an atom or ion to an ion capable of producing energy holes for shrinking hydrogen atoms are given in the following table. The sum of an ionization energy, IE n , plus the next consecutive ionization energy, IE n +ι, of the electron donating atom or ion minus the sum of the first ionization energy, IEι, and the electron affinity, EA, of the electron accepting ion equals approximately 27.21 eV. In another embodiment, a catalytic system that provides an energy hole hinges on the transfer of two electrons from an atom, ion, or molecule to another atom, ion, or molecule such that the sum of two ionization energies minus the sum of two ionization energies of the participating atoms and/or molecules is approximately 27.21 eV A catalytic system that hinges on the transfer of two electrons from a first ion to a second ion involves sιlver( Ag + ) and silver (Ag 2 + ) For example, the second and third ionization energies of silver are 2149 eV and 5483 eV, respectively And, the second and first ionization energies of silver are 2149 eV and 758 eV, respectively The energy hole resulting from a two electron transfer is appropriate for resonant absorption. The combination of Ag + to Ag 3+ and Ag 2+ to Ag, then, has a net energy change of 27.25 eV. 27.25 eV + Ag + + Ag2 + + H[^ J - Ag 3+ + Ag + H[ ( & ° } ) ] + Up + 1 ) 2 - p 2 ] x 13.6 eV Catalytic systems that hinge on the transfer of two electrons from an atom, or ion to an ion capable of producing energy holes for shrinking hydrogen atoms are given in the following table. The sum of an ionization energy, IE n , plus the next consecutive ionization energy, IE n +ι, of the electron donating atom or ion minus the sum of an ionization energy, IE m +ι, Plus the next consecutive lower ionization energy, IE , of the electron accepting ion equals approximately 27.21 eV. 29 33 Ru 1676 2847 Ho 2+ 1180 602 Ru 2741 1676 2847 Er 2+ 1193 610 Rh ι + 2720 1808 3106 V 2+ 1465 674 Rh 2775 1808 3106 b 2+ 1 32 688 » Rh 2794 1 + 1808 3106 Sn 2+ 14.63 734 Rh 2716 1808 3106 Hf 2+ 1490 660 Pd 1 + 2764 19.43 32.93 Al 2+ 18.83 5.99 Pd 1 + 27.55 19.43 32.93 Si 2+ 16.34 8.15 Pd ] + 27.86 19.43 32.93 Fe 2+ 16.18 7.87 28.31 Pd ] + 19.43 32.93 Co 2+ 17.06 7.86 Pd 1 + 27.44 19.43 32.93 Ru 2+ 16.76 7.37 Pd 1 + 28.23 19.43 32.93 In 2+ 18.87 5.79 27.71 ' Pd 1 + 19.43 32.93 Sb 2+ 16.53 8.64 27.19 Pd 1 + 19.43 32.93 Bi- 2+ 16.69 7.29 28.38 Ag 1 + 21.49 34.83 Cu 2+ 20.29 7.73 28.30 Ag 1 + 21.49 34.83 As 2+ 18.63 9.81 27.88 Ag 1 + 21.49 34.83 Ag 2+ 21.49 7.58 27.25 Ag 1 + 21.49 34.83 Cs 2+ 25.10 3.89 27.33 Ag 1 + 21.49 34.83 ng 2+ 18.76 10.44 27.13 Cd 1 + 16.91 37.48 Zn 2+ 17.96 9.39 Cd 1 + 27.03 16.91 37.48 Ga 2* 20.51 6.00 Cd 1 + 27.88 16.91 37.48 Cd 2+ 16.91 8.99 Cd 28.49 16.91 37.48 TI 2+ 20.43 6.11 In 27.85 18.87 28.03 Sc 2+ 12.80 6.54 27.56 In 1 + 18.87 28.03 Y 2+ 12.24 6.38 28.28 In 1 + 18.87 28.03 Yb 2+ 12.18 6.25 28.47 In ] t 18.87 28.03 Lu 2+ 13.90 5.43 27.57 In 2+ 28.03 54.00 Sr 3+ 43.60 11.03 27.40 In 2+ 28.03 54.00 Cd 3+ 37.48 16.91 27.64 Sn 1 + 14.63 30.50 Ca 2+ 11.87 611 2715 Sn 1+ 1463 3050 Sr 2+ 11.03 5.70 1 + 2841 Sn 1463 3050 La 2* 11.06 558 28.50 Sn 1 + 1463 3050 Sm 2* 1107 563 2843 Sn 1+ 1463 3050 Eu 2* 11.24 567 1 + 28.23 Sn 1463 3050 Tb 2t 11.52 585 27.76 Sn 1 + 1 63 3050 Dy 1167 593 27.54 In another embodiment, a catalytic system that provides an energy hole hinges on the transfer of three electrons from an ion to another ion such that the sum of the electron affinity and two ionization energies of the first ion minus the sum of three ionization energies of the second ion is is approximately 27.21 eV. A catalytic system that hinges on the transfer of three electrons from an ion to a second ion involves Li " and Cr 3 + . For example, the electron affinity, first ionization energy, and second ionization energy of lithium are 0.62 eV, 5.392 eV, and 75.638 eV, respectively And, the third, second, and first ionization energies of Cr 3 + are 30.96 eV, 16.50 eV, and 6.766 eV, respectively The energy hole resulting from a three electron transfer is appropriate for resonant absorption The combination of Li " to Lι 2 + and Cr 3 + to Cr, then, has a net energy change of 27 42 eV 27 42 eV + Li " + Cr 3 + + 1 + U p + 1 ) 2 - p 2 ] x 13 6 eV (68) Lι 2 + + Cr → Lr Cr^* t 27 42 eV (69) And, the overal l reaction is H H [(p + I ) 2 -P 2 J x 13 6 eV (70) . ( P Three Electron Transfer(Two Species) 40 In another embodiment, a catalytic system that provides an energ hole hinges on the transfer of three electrons from an atom, ion, or molecule to another atom, ion, or molecule such that the sum of three consecutive ionization energies of the electron donating species minus the sum of three consecutive ionization energies of the e lectron accepting species is approximately 27.21 eV A catalytic system that hinges on the transfer of three electrons from an atom to an ion involv Ag and Ce 3 + . For example, the first, second, and third ionization energies of silver are 7.58 eV, 21.49 eV, and 34.83 eV, respectively. And, the third, second, and first ionization energies of Ce 3+ are 20.20 eV, 10.85 eV, and 5.47 eV, respectively. The energy hole resulting from three electron transfer is appropriate for resonant absorption. The combination of Ag to Ag 3 + and Ce 3+ to Ce, then, has a net energy chang of 27.38 eV. 27.38 eV + Ag + Ce 3 + + H ^ 1 - Ag 3 + + Ce + H[ ( ^ ^ 1 + Up + 1 ) 2 - p 2 ] x 13.6 eV (7 Ag 3 + + ce - Ag + Ce 3+ + 27.38 eV (7 And, the overall reaction is H i ] → H ( p t° 1 ) 1 + f ( P + ' )2 - p J 13.6 eV ( 7 Catalytic systems that hinge on the transfer of three electrons from an atom, or ion to an ion capable of producing energy holes for shrinking hydrogen atoms are given in the following table. The sum of three consecutive ionization energies, IE n + 1 En-*- 1 + IE n +2, of the electron donating species, DS, minus three consecutive ionization energies, IE + + IEm+ ι + IEm, of the electron accepting species, AS, equals approximately 27.21 eV. 41 N 1691 899 28 20 N 1876 1044 28 1 N 4530 2556 27 66 0 2381 1297 27 28 0 28 36 0 27 80 0 27.70 F 27.55 F 27.55 e 28.09 Na 27.5 1 Na 28.20 Al 28.43 Si 27.90 Si 27. 1 7 Si 27.14 P 28.03 P 28.04 P 27.88 S 28.42 S 28. 12 S 27.86 S 27.75 S 28.23 S At 38.30 25.04 14.32 27.80 S A 42.50 22.84 11.80 28.32 S At 42.60 22.74 11.93 28 1 9 S At 4270 23.68 1205 2703 S 5+ 5600 4530 2556 27.95 Cl 3+ 2749 1358 682 2850 Cl 4+ 4640 2716 1615 2717 Cl 4+ 4232 3194 1503 2759 Ar 3+ 3367 1564 743 2739 Ar 3+ 2835 .1863 981 2733 Ar 3+ 3106 1808 746 2753 Ar 3+ 2983 2043 611 2776 42 AA In a further embodiment, an energy hole of energy equal to the total energy released for a below "ground state" electronic transition of the hydrogen atom is provided by the transfer of an electron between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises tne transfer of an electron from one species to another species whereby the sum of the ionization energy of the electron donating species minus the ionization energy or electron affinity of the electron accepting species m equals approximately 27.2 1 eV; where m is an integer. For m = 3 corresponding to the n = 1 to n = 1 /2 transition, an eff icient catalytic system that hinges on the coupl ing of three resonator cavities involves arsenic and cal cium For example, the third ioni zation energy of calcium is 50 908 eV Th is energy hol ' e is obviously too high for resonant absorption However, As( l ) re leases 9.8 1 eV when it is 47 reduced to As The combination of Ca 2 + to Ca 3 + and As + to As, then, ha a net energy change of 41 1 eV 4 1 1 eV + As + + Ca + + H a o - As + Ca^ + ] x 1 3 6 P J L ( P ) ] ' ( p + 1 ) 2 - p2 eV (74 AS + Ca 3 As + + Ca 2 + + 41 1 eV (75 And, the overall reaction is 0_ H H [(p + 1 )2 -p2] x 13.6 eV (76 L P J L(P + 1 ) Catalytic systems that hinge on the transfer of an electron from an atom or ion to another atom or ion capable of producing energy holes of approximately AO.β eV corresponding in energy to the n = 1 to the n = 1 /2 electronic transition of hydrogen are given in the fol lowing table. The ionization energy of the electron donor, IE n , minus the ionization energy of the electron acceptor, IE , equal approximately 40.8 eV. An energy hole is provided by the transfer of multiple electrons between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one or more species whereby the sum of the ionization energies and/or electron aff inities of the electron donating species minus the sum of the ionization energies and/or electron aff inities of the electron acceptor m species equals approximately 27 2 1 eV where. m and t are integers 48 THE NATURE OF THE CHEMI CAL BOND Of HYDROGEN-TYPE MOLECULES AND MOLECULAR IONS Two hydrogen atoms react to form a diatom ic molecule, the hydrogen molecule 2 H[a 0 ] → H 2 [2C = y β a 0 ] (77 where 2c ' is the internuclear distance. Also, two hydnno atoms react t form a diatomic molecule, a dihydrino molecule. 2 H H*2 2c ' = 5 (78 where p is an integer. Hydrogen molecules form hydrogen molecular ions when they are singly ionized. H 2 [2C = \[2 a 0 ] → H 2 [ 2C = 2a 0 ] + + e- (79 Also, dihydrino molecules form dihydrino molecular ions when they are singly ionized. H*2, 2C = - - 2 [ 2C - + e- (80 The Hvdrooen-Tvpe Molecular Ions Each hydrogen-type molecular ion comprises two protons and an electron where the equation of motion of the electron is determined by the central field which is p times that of a proton at each focus (p is one for the hydrogen molecular ion, and p is an integer greater than one for each dihydrino molecular ion). The differential equations of motion in the case of a central field are m(r - rθ 2 ) = f(r) (81 m(2rθ + rθ ) = 0 (82) The second or transverse equation, Eq (82), gives the result that the angular momentum is constant Γ Θ = constant = L/m (83) where L is the angular momentum ( h in the case of the electron). The central force equations can be transformed into an orbital equation by 1 the substitution, u = - The differential equation of the orbit of a particle moving under a central force is δ 2 u -1 — +u = — --^-f(u _ 1 ) (84 ) δθ 2 rnL^u 2 m2 Because the angular momentum is constant, motion in only one plane need be considered, thus, the orbital equation is given in polar coordinates The solution of Eq (84) for an inverse square force f(r) = - " " (85) is (86) (87) k (l * e) (88) where e is the eccentricity of the ellipse and A is a constant. The equation of motion due to a central force can also be expressed in terms of the energies of the orbit. The square of the speed in polar coordinates is v 2 = (r2 + Γ 2Θ2 ) (89) Since a central force is conservative, the total energy, E, is equal to the sum of the kinetic, T, and the potential, V, and is constant The total energy is — m (r-2 + r θ ) + v(r) = E = constant (90) 1 Substitution of the variable u = - and Eq (83) into Eq (90) gives the orbital energy equation 1 L 2 δ 2 u , . — m— -[( ~ ^) + u 2 + V(u " l) = E (91) m 2 δθ 2 Because the potential energy function V(r) for an inverse square force field is 50 V(r) u (92 the energy equation of the orbit, Eq (91 ), L 2 δ-^u nrr ) t X } - Ku = E 2 (93 m- δθ 2 which has the solution where the eccentricity, e, is L e = [ 1 + 2Em-^-i<-2 ] "2 (95) m2 Eq. (95) permits the classification of the orbits according to the total energy, E, as follows: E < 0, e < 1 closed orbits (el l ipse or circle) E = 0, e = 1 parabolic orbit E > 0, e > 1 hyperbol ic orbit Since E = T + V and is constant, the closed orbits are those for which T < I VI, and the open orbits are those for which T ≥ I VI. It can be shown that the time average of the kinetic energy, < T >, for ell iptic motion in an inverse square field is 1 /2 that of the time average of the potential energy, < V >. < T > = 1 /2 < V >. As demonstrated in the One Electron Atom Section of The Unification of Spacetime. the Forces. Matter, and Energy. Mil ls, R., Technomics Publ ishing Company, Lancaster,, PA, ( 1 992), the electric inverse square force is conservative; thus, the angular momentum of the electron, h, and the energy of atomic orbitspheres is constant. In addition, the orbitspheres are nonradiative when the boundary condition The central force equat ion, Eq (90), has orbi tal solut ions which are circular, el liptic, parabolic, or hyperbol ic The former two types of solutions are associated with atomic and molecular orbitals These solutions are nonradiative The boundary condi tron for nonradiation given in the One Electron Atom Sect ion of The Uni ficat ion of Spacet ime. the Forces, Matter, and Energy. Mi l ls, R , Technomics Publ ishing Company, Lancaster, PA, ( 1992), is the absence of components of the space-time Fourier transform of the charge density function synchronous with waves travel ing at the speed of l ight The boundary condition i s met when the velocity for every point on the orbitsphere is v rι = — ( 96 ) m e r n The allowed velocities and angular frequencies are related to r n by Vn = r n ω n (97) h ω n (98) m e rv As demonstrated in the One Electron Atom Section and by and Eq. (8.17) of The Unification of Spacetime. the Forces. Matter, and Energy. Mil ls, R., Technomics Publishing Company, Lancaster, PA, ( 1992), this condition is met for the product function of a radial Dirac delta function and a time harmonic function where the angular frequency, ω, is constant and given by Eq. (98). πL ωn = ^2 = ( 99 ) where L is the angular momentum and A is the area of the closed geodesic orbit. Consider the solution of the central force equation comprising the product of a two dimensional ellipsoid and a time harmonic function. The spatial part of the product function is the convolution of a radial Dirac delta function with the equation of an ellipsoid. The Fourier transform of the convolution of two functions is the product of the individual Fourier transforms of the functions; thus, the boundary condition is met for an el lipsoidal-time harmonic function when πh h ton = — - = ( 1 00) n m e A m e ab where the area of an ellipse is A = πab ( 10 1 ) where 2b is the length of the sem iminor axis and 2a is the length of the semimajor axis The geometry of molecular hydrogen is el liptic with the internuclear axis as the principle axis, thus, the electron orbital -is a two dimensional el lipsoidal-time harmonic function The mass follows geodesies time harmonically as determined by the central field of the 9873 52 protons at the foci Rotat ional symmetry about the internuclear axis further determines that the orbital is a prolate spheroid In general, el l ipsoidal orbits of molecular bonding, hereaf ter referred to as ell ipsoidal molecular orbitals (M 0 's), have the qeneral equation χ2 y2 z 2 + -X- t — - = 1 ( 10 a 2 b 2 c 2 The semipπnciple axes of the ell ipsoid are a, b, c. In el lipsoidal coordinates the Laplacian is An ellipsoidal M. 0. is equivalent to a charged conductor whose surface given by Eq. ( 102). It carries a total charge q, and it's potential is a ' solution of the Laplacian in ellipsoidal coordinates, Eq. ( 103). Excited states of orbitspheres are discussed in the Excited State of the One Electron Atom (Quantization) Section of The Unification of Spacetime. the Forces. Matter, and Energy. Mills, R., Technomics Publishing Company, Lancaster, PA, ( 1992). In the case of ellipsoidal M. 0. 's, excited electronic states are created when photons of discrete frequencies are trapped in the ellipsoidal resonator cavity of the M. 0. The photon changes the effective charge at the M. 0. surface where the central field is ellipsoidal and arises from the protons and the effectiv charge of the trapped photon at the foci of the M. 0. Force balance is achieved at a series of ellipsoidal equipotential two dimensional surfaces confocal with the ground state ellipsoid. The trapped photons are solutions of the Laplacian in ellipsoidal coordinates, Eq. ( 103). As is the case with the orbitsphere, higher and lower energy state are equally valid The photon standing wave in both cases is a solution of the Laplacian in ell ipsoidal coordinates. For an ellipsoidal resonator cavity, the relationship between an allowed circumference, 4aE, and the photon standing wavelength, λ, is 4aE = nλ ( 10 where n is an integer and where a 2 - b k = ~ : ( 10 is used in the elliptic integral E of Eq (104) Applying Eqs (104) and (105), the relationship between an allowed angular frequency given by Eq (100) and the photon standing wave angular frequency, ω, is πh _ h h_ _ J_ m e A = n-iena ^ nb, = m e 3nbn = n 2 ω ' = ω n (106) where n = 1, 2, 3, 4, 1 1 1 n 2 ' 3 ' 4 ' - ωι is the allowed angular frequency for n = 1 3] and b] are the allowed semimajor and semiminor axes for n = 1 Let us compute the potential of an ellipsoidal M.0. which is equivalent to a charged conductor whose surface is given by Eq. (102). It carries a total charge q, and we assume initially that there is no external field We wish to know the potential, φ, and the distribution of charge, σ, over the conducting surface. To solve this problem a potential function must be found which satisfies Eq. (103), which is regular at infinity, and which is constant over the given ellipsoid. Now ξ is the parameter of a family of ellipsoids all confocal with the standard surface ξ= 0 whose axes have the specified values a, b, c. The variables ζ and η are the parameters of confocal hyperboloids and as such serve to measure position on any ellipsoid ξ= constant. On the surface ξ= 0; therefore, φ must be independent of ζ and η. If we can find a function depending only on ξ which satisfies Eq. (103) and behaves properly at infinity, it can be adjusted to represent the potential correctly at any point outside the ellipsoid ξ= 0. Let us assume, then, that φ=φ(ξ). The Laplacian reduces to — (Rξ^) = 0 Rξ= (ξ + a 2 ) (ξ + b2) (ξ + c 2 ) (107) which on integration leads to I δξ φ ( ξ ) = C 1 J ~ (108) Rξ where Ci is an arbitrary constant The choice of the upper limit is such as to ensure the proper behavior at infinity When ξ becomes very large, Rξ approaches ξ 3 /- and 54 On the other hand, the equation of an ellipsoid can be written in the for If r = χ2 + y2 + z 2 1S the distance from the origin to any point on the ellipsoid ξ, it is apparent that as ξ becomes very large ξ→r^ and hence at great distances from the origin 2Cι Φ — ( 111 The solution Eq. (108) is, therefore, regular at infinity. Moreover Eq. ' (111) enables us to determine at once the value of Ci; for it has been shown that whatever the distribution, the dominant term of the expansion at remote points is the potential of a point charge at the origin equal to the total charge of the distribution - in this case q. q Hence C\ = - — , and the potential at any point is σπεo OO 0 r δξ The equipotential surfaces are the ellipsoids ξ = constant. Eq. (112) is a elliptic integral and its values have been tabulated (See for example, Jahnke-Emde, Tables of Functions.2nd ed., Teubner, (1933)). To obtain the normal derivative we must remember that distance along a curvilinear coordinate u 1 is measured not by du 1 but by hjdu'. I ellipsoidal coordinates δφ 1 δφ_ - g 1 δn " h i δξ ~ 4πε 0 / ( ξ - η ) ( ξ - ζ) The density of charge, σ, over the surface ξ = 0 is Defining x, y, z in terms of ξ,η.ζ we put ξ = 0, it may be easily verified that x 2 y 2 z 2 ζη Consequently, the charge density in rectangular coordinates is (The mass densi ty function of an M. 0. is equivalent to its charge density function where m replaces q of Eq. ( 1 17)). The equation of the plane tangent to the ell ipsoid at the point xo, yo, zo s *o Yo z o χ ? + γ " + z = ] ( i i 8 a 2 b c 2 where X, Y, Z are running co-ordinates in the plane. After dividing through by the square root of the sum of the squares of the coefficients of X, Y, and Z, the right member is the distance D from the origin to the tangent plane. That is, so that σ = , D ( 120 4πabc In other words, the surface density at any point on a charged ellipsoidal conductor is proportional to the perpendicular distance from the center of the ellipsoid to the plane tangent to the ellipsoid at the point. The charge is thus greater on the more sharply rounded ends farther away from the origin. In the case of hydrogen-type molecules and molecular ions, rotational symmetry about the internuclear axis requires that two of the axes be equal. Thus, the M. 0. is a spheroid, and Eq. ( 1 12) can be integrated in terms of elementary functions. I f a > b = c, the spheroid is prolate, and we f ind for the potential φ Spheroidal Force Equations El ectric Force 56 The spheroidal M 0 is a two dimensional surface of constant potential given by Eq ( 121 ) for ξ= 0 For an isolated electron M 0 the electric field inside is zero as given by Gauss' Law where the charge density, p, inside the M 0 is zero Gauss' Law at a t dimensional surface is n • ( 6ι - 62 ) = - ( 12 εo £2 is the electric field inside which is zero The electric field of an ellipsoidal M. 0. is given by substituting σ given by Eq ( 1 14) and Eq. (-1 1 into Eq. ( 123). The ele ε From Eqs. ( 106), the magnitude of the elliptic field corresponding to a below "ground state" hydrogen-type molecular ion is an integer. T integer is one in the case of the hydrogen molecular ion and an integer greater than one in the case of each dihydrino molecular ion. The centra electric force from the two protons, Fe, is where p is one for the hydrogen molecular ion, and p is an integer greate than one for each dihydrino molecule and molecular ion. Centripetal Force Each infinitesimal point mass of the electron M 0 moves along a geodesic orbit of a spheroidal M 0 in such a way that its eccentric angle, θ, changes at a constant rate That is θ = ωt at time t where ω is constant, and r(t) = lacos ωt + ibsin ωt ( 12 is the parametric equation of the ellipse of the geodesic If a(t) denotes the acceleration vector, then In other words, the acceleration is centripetal as in the case of circular motion with constant angular speed ω The centripetal force, Fς, is F c = ma = -mω 2 r(t) ( 129 Recall that nonradiation results when ω = constant given by Eq. (106). Substitution of ω given by Eq. (106) into Eq. (129) gives where D is the distance from the origin to the tangent plane as given " by Eq. (119). If X is defined as fol Then, it follows from Eqs. (114), (120), (124), and (126) that D = 2ab2χ (132) Force balance between the electric and centripetal forces is which has the parametric solution given by Eq. (127) when 2a 0 a = " jT- (134) Energies of Hydrogen-Type Molecular Ions From Eqs. (106), the magnitude of the elliptic field corresponding to a below " ground state " hydrogen-type molecule is an integer, and the integer The potential energy, Ve, of the electron M.0. in the field of magnitude p times that of the protons at the foci (ξ = 0) is where a 2 - b 2 = c ' (136) 9873 58 2C is the distance between the foci which is the internuclear distance The kinetic energy, T, of the electron M 0 is given by the integral of th _. 2 2 lπ a + v a 2 - b 2 ( 13 m e a v a 2 - b 2 a - a 2 - b 2 From the orbital equations in polar coordinates, Eqs (86-88), the following relationship can be derived L2 (13 For any ellipse, Thus, (polar coordinates) (140 Using Eqs. (130) and (137), and (92) and (137), respectively, it can be appreciated that b of polar coordinates corresponds to c' =V a 2 - b 2 of elliptic coordinates, and k of polar coordinates with one attracting focu is replaced by 2k of elliptic coordinates with two attracting foci. In elliptic coordinates, k is given by Eq. (124) and (126) 2pe k = — — (141 4πεo and L for the Substitution of a given by Eq (134) into Eq (142) is a 0 (143 C = " p ~ 2a 0 The internuclear distance from Eq (143) is 2C = P One half the length of the semiminor axis of the t prolate spheroidal M 0, b = V/aa2^ -- c ' ^ (144 Substitution of a = -— - and C = -- into Eq (144) b = V5 a , -, (145) P The eccentricity, e, is e = ~ (146) 2ao ao Substitution of a = ——and c " = — ~ into Eq. (146) is 1 e = 2 (147) The potential energy, Vp, due to proton-proton repulsion in the field of magnitude p times that of the protons at the foci (ξ = 0) is Substitution of a and b given by Eqs. (134) and (145), respectively, into Eqs. (135), (137), and (148) is p2 e 2 V p = - — (150) H βπεoao 2p e 2 T = a X. In 3 (151) oπεoao Eτ = V e + V p + T (152) ET = 13.6 eV ( -4p 2 ln3 + p 2 + 2p 2 ln3 ) (153) The bond dissociation energy, EQ, is the difference between the binding energy of the corresponding hydrogen atom or hydrino atom and Ej- ED = E( iH|τ I )- - ET (154) Vibration It can be shown that a perturbation of the orbit determined by an inverse square force results in simple harmonic oscillatory motion of the orbit. For the case of a circular orbit of radius a, an approximation of the angular freque ω- (,55) 29873 60 Osci l lating charges radiate However, molecules and molecular ions including the hydrogen molecule, the hydrogen molecular ion, dihydrino molecules, and dihydrino molecular ions demonstrate nonradiative zero order vibration which is time harmonic osc i l lat ion of the posit ion of th protons along the principle axis The protons are located at the foci, an nonradiat ion is due to the geometry of the el l ipse where the electron M 0 is el l ipsoidal A fundamental property of an ellipse is that a light ra emitted from a focus in any direction is reflected off of the el lipse to the other focus, and the sum of the lengths of the ray paths is constant, 2a. An oscil lating charge ro(t) = d sinωot has a Fourier spectrum qcood J( k,ω) = ~ ~ Jm(kcosθ d){δ[ω - (m + 1 )ω<> ] + δ[w - (m- 1 )ωoJ] ( 15 where Jm 's are Bessel functions of order m. These Fourier components can, and do, acquire phase velocities that are equal to the velocity of light. Consider two oscillating charges at the foci of an ellipsoidal resonator cavity, an ellipsoidal M. 0. A nonradiative standing electromagnetic wave can be excited which has higher order harmonics in addition to the fundamental frequency as given in Eq. ( 156). This nonradiative standing wave gives rise to zero order vibration of the molecule. The zero order mode is a standing wave with destructive interference of all harmonics of the fundamental frequency, ωo. A ray undergoes a 180° phase shift upon reflection, and the protons oscil late in opposite relative directions. Thus, mutual destructive interference occurs when x, the distance from one focus to the other for a reflected ray is equal to a wavelength, λ, where λ is . ( 157 ( 158 ( 159 ( 160 The vibrational energy of the protons, E Pv )b , is equal to the maximum vibrational kinet ic energy of the protons Substitution of Eqs ( 158) and ( 159) into Eq ( 160) and multipl ication by two corresponding to the two protons is 1 h 2 i — „ h 2 T = τ max = 2 o m— ΪX ( 2 ) 2 = 2 ( 16 1 The vibrational energy is the sum of the vibrational energy of the electron M 0 and that of the protons which are equal 4h2 E vib = — 9 ( 162 V1D mx 2 where m is the sum of the masses of the protons, each of mass mp. m = m p ( 163) And, X is 2a. Thus, the vibrational energy is ( 164) ( 165) The time average internuclear distance is increased by the zero order vibration because the total energy verses internuclear distance function is asymmetrical with a lower slope for internuclear distances greater than the internuclear distance at which the total energy is a m inimum. Elongation occurs along the principle axis, and shifts the the total energy verses internuclear distance function to a new function which includes the contribution due to vibration. The perturbation of ET, the total energy of the M. 0. given by Eq. ( 152) with a fractional increase in the semimajor axis, a, and the reciprocal decrease in the semiminor axis, b is calculated by reiteration The angular frequency of the M.O given by Eq ( 1 00) is unchanged when a and b are changed by reciprocal fractions The corrected a and b are obtained when the change in ET IS equal to the vibrational energy The vibrational energy i s the sum of two equal components, the v ibrat ional energy of the protons and the vibrational energy of the electron M 0 Vibration causes a redistribution of energy within the molecule The M O potential and kinetic energy terms given by Eqs ( 1 35), ( 1 37), and ( 148) add π radians out of phase with the potential and kinetic energies of vibration, thus, the energy of the molecule wi l l decrease by this amount whi ch is equal to one half the 62 vibrational energy An x% increase in the semimajor axis and the rec iprocal decrease in the semiminor axis decreases ET by the vibrational energy and releases energy equal to one half vibrational energy x , 2ao 1 3 Substitution of a = ( 1 + x x) ~ — and b = ~ — a 0 into Eqs ( 1 + Toό ) (149), (150), (151), and (152) and (154) with the reduction of the total energy by one half the vibrational energy is 3 0 ED = E( H ~ ETzero order 166 LP J Eq. ( 166) is the bond dissociation energy where E v1 is given by Eq. ( 167). Substitution of a = ( 1 + Γ^Γ) — " into Eq. ( 165) is Zero order vibration arises because the state is nonradiative and is an energy minimum. Furthermore, electromagnetic radiation of discrete energies given by Eq. ( 165) can be trapped in the resonator cavity where constructive interference occurs at the foci. These standing waves change the electric field at the ellipse surface as described in the Excited States Section of The Unification of Spacetime. the Forces. Matter, and Energv. Mills, R., Technomics Publishing Company, Lancaster, PA, ( 1992); thus, the major and minor axes increase and the total energy of the molecule given by Eqs. ( 149), ( 150), ( 151 ), and ( 152) increases. The photons of these standing waves drive the vibration of the molecule at a higher frequency than the zero order frequency, but are reradiated. The energy of a vibrational transition is given by the difference of the sum of the energies of the modes excited before and after the transition. The modes are quantized, and from Eq ( 165), the energy spacing of the modes is closer together as the total vibrational energy increases Excited Electronic States of Ellipsoidal M 0 's Excited states of orbi tspheres are discussed in the Excited States of the One Electron Atom (Quantization) Sect ion of The Unif icat ion of Spacetime. the Forces. Matter, and Energy. Mi l ls, R , Technomics Publishing Company, Lancaster, PA, ( 1 992) In the case of el l ipsoidal M 0 's, exci ted electronic states are created when photons of discrete frequencies are trapped in the el lipsoidal resonator cavity of the M 0. The photon changes the ef fect we charge at the l 0 surface where the central field is el lipsoidal and arises from the protons and the effective charge of the trapped photon at the foci of the M 0 Force balance is achieved at a series of ellipsoidal equipotential two dimensional surfaces confocal with the ground state ellipsoid. The trapped photons are solutions of the Laplacian in ellipsoidal coordinates, Eq. ( 103). Magnetic Moment of an Ellipsoidal M. 0. The magnetic dipole moment,μ, of a current loop is μ = iA ( 168) The area of an ell ipse is given by Eq. ( 101 ). For any elliptic orbital due to a central field, the frequency, f, is _L_ where L is the angular momentum. The current, i, is eL_ where e is the charge. Substitution of Eqs. ( 170) and ( 101 ) into Eq. ( 168) where L is the angular momentum of the electron, h ,is eh < "X= ( ,7, ) which is the Bohr magneton. Magnetic Field of an El lipsoidal M. 0 The magnetic field can be solved as a magnetostatic boundary value problem which is equivalent to that of a uniformly magnetized ellipsoid (See Stratton, J. A , Electromagnetic Theory. McGraw-Hi l l Book Company, ( 1941 ), p 257) The magnetic scalar potential inside the el l ipsoidal M. 0., φ " , is 9873 64 _e _ ds Φ- 2m ( x f - ( 17 o J 0 (s + 3 2 )R The magnetic scalar potential outside of the M. 0., φ + , is The magnetic f ield inside the ell ipsoidal M. 0., H x , is - _ _δcjr _ -eh r ddss H x " " δx = 2me 0 J J ( (ss ++ a a 2 4)RR s c- The magnetic field inside the el l ipsoidal M. 0. is uniform and parallel to the minor axis. HYDROGEN-TYPE MOLECULES Force Balance Hydrogen-type molecules comprise two indistinguishable electron bound by an elliptic field. Each electron experiences a centrifugal force and the balancing centripetal force (on each electron) is produced by th electric force between the electron and the elliptic electric field and the magnetic force between the two electrons causing the electrons to pair. In the present case of hydrogen-type molecules, if the eccentricit equals -j== , then the vectorial projection of the magnetic force betwee the electrons, of Eq. (3.15) of the Two Electron Atom Section of The Unification of Spacetime. the Forces. Matter, and Energy. Mills, R., Technomics Publ ishing Company, Lancaster, PA, ( 1992), is one. The molecules wi ll be solved by self consistency. Assume e = -j=, then the force balance equation given by Eq. (3. 18) of the Two Electron Atom Section of The Unification of Spacetime. the Forces. Matter, and Energy. Mil ls, R., Technomics Publishing Company, Lancaster, PA, ( 1992) and Eq. ( 133) is 2ao ao 65 3θ a = - (17 Substitution of Eq (177) into (142) is 1 c = --#= a 0 (17 P V 2 Substitution of Eqs (177) and (178) into Eq (144) is 1 b = c = r= a 0 (17 P V 2 Substitution of Eqs. (177) and (178) into Eq. (146) is e = -J= ( 18 The eccentricity is -j= ; thus, the present self consistent solution • which was obtained as a boundary value problem is correct. The internuclear distance given by multiplying Eq. (178) by two is Energies of the Hydrogen-Type Molecules The energy components defined previously for the molecular ion, Eqs. (149-153), apply in the case of the corresponding molecule. And, each molecular energy component is given by the integral of corresponding force in Eq. (175) where each energy component is the total for the two equivalent electrons. The parameters a and b are give by Th ET = V e + T + V m + V p (185 E ( 2 H -2ρ 2 13.6 eV (18 The bond dissociation energy, ED, IS the difference between the binding energy of the corresponding hydrogen atoms or hydrino atoms and ET- As in the case of the hydrogen-type molecular ion, the time averaged internuclear distance is increased by the zero order molecular vibration. A y% increase in the semimajor axis and the reciprocal decrease in the semiminor axis releases energy which is equal to one half the vibrational energy. Substitution of a = ( 1 + ao into Eqs. (181-188) with the reduction of the total energy by one half the vibrational energy is : vib ED = E( #] > - ET zero order (189 Eq. (189) is the bond dissociation energy where E vib is given by Eq. (190). y a o Substitution of a = (1 + TX^) XT into Eq. (165) is OO 7 p 0.59 -vib eV (190 -Y_ N ap_ (1 00 p THE HYDROGEN MOLECULAR IO H2[2C = ^2 a 0 ] + Force balance between the electric and centripetal forces is given by Eq (133) where p = 1 h2 .2 2ab 2 x = m e a b2 — ■ ■ πεo X (191 which has the parametric solution given by Eq. (127) when a = 2a 0 (192 The semimajor axis, a, is also given by Eq (134) where p = 1 The internuclear distance, 2c', which is the distance between the foci is given by Eq ( 143) where p = 1 2c ' = 2a 0 (193 The experimental internuclear distance is 2ao The semiminor ax The eccentricity, e, is given by Eq. (147). e= 2 (195 Energies of the Molecular Hydrogen Ion The potential energy, Ve, of the electron M.0. in the field of the protons at the fo The potential energy, Vp, due to proton-proton repulsion is given by Eq. (148) where p = 1 e V = o 1 ( 97 P δπεo^ a 2 - b 2 The kinetic energy, T, of the electron M.0. is given by Eq. (137) where p = 2fi a + a2 - b2 T= . In 1 (198 m e a"v a 2 - b 2 a - a 2 - b 2 Substitution of a and b given by Eqs. (192) and (194), respectively, into Eqs. (196), (197), and (198) is -4e 2 V e = — In 3 = -59.763eV (199) δπεoao v P = δ^ 13 - 6 eV (200) T = Q 2θ In 3 = 29.88 eV (201) πεoao ET = V e + V p + T ( 202) ET = -16.282 eV (203) E( H[a 0 ] ) = -13.6 eV ET = V e t Vp + T (204) ET = 1 3 6 eV ( -41n3 + 1 + 21n3 ) (205) The bond dissociat ion energy, ED, is the difference between the binding energy of the corresponding hydrogen atom and ET ED = E( H[ aJ ) - ET = 2 68 eV (206) Eqs ( 199-206) are equivalent to Eqs ( 149- 154) where p = 1 Vibration It can be shown that a perturbation of the orbit determined by an inverse square force results in simple harmonic oscillatory motion of the orbit. Zero order vibration arises because the state is nonradiative and is an energy minimum. The time average internuclear distance is. increased by the zero order vibration. A 0.1 % increase in the semimajor axis and the reciprocal decrease in the semiminor axis decreases ET by the vibration energy and releases energy equal to one half the vibrational energy. Substitution of a = 2.002 ao and b = 1.7303 ao into Eqs. ( 196), ( 197), ( 198), and (204) and (206) with the reduction of the total energy by one half the vibrational energy is E D = E ( H[a 0 ] ) - ETzero order " ~ ψ = 2.76 eV ( 207 ) Eq. (207) is the bond dissociation energy where E vlb is given by Eq. (206). The experimental value is 2.7δ eV. Substitution of a = 2.002 ao into Eq. ( 165) is E vjb = 0.147 eV (20δ) THE HYDROGEN MOLECULE H 2 [2C = a 0 ] Force Balance The force balance equation for the hydrogen molecule is given by Eq ( 175) where p = 1 R2 e 2 h2 me a2 b 2 2 ^ab υ2 x Λ = - 4 — πεo X Λ + ^ 2-m— e a ^b2 9 2ab 2 x (209) which has the parametric solution given by Eq ( 127) when a = a 0 (21 0) The semimajor axis, a, is also given by Eq ( 177) where p = 1 The internuclear distance, 2c ' , which is the distance between the foci is given by Eq ( 178) where p = 1 2C = ΛT ~ 2 a 0 (21 1 ) 69 The experimental internuclear distance is V ~ 2 ~ ao The semiminor axis is given by Eq (179) where p = 1 1 t> = -f= a 0 ( 21 V 2 The eccentricity, e, is given by Eq (180) e = -τ== (21 V 2 Energies of the Hydrogen Molecule The energies of the hydrogen molecule are given by Eqs (181-187) where p = 1 -2e 2 a + a 2 - b 2 V e = j in , = -67.813 eV (21 δTrεo a 2 - b 2 a - a 2 - 2 The energy, Vm , of the magnetic force is Vm = -169533 eV (217 E T = V e + T + V m + V p (21 δ Eτ = -136ev[(2V2 - V2 + jln ^j- - 2 -3163 eV (219 E( 2 H[a 0 ] ) = -27.21 eV (220 The bond dissociation energy, ED, IS the difference between the binding energy of the corresponding hydrogen atoms and ET ED = E( 2 H[a 0 ] )- Eτ = 443 eV (221 As in the case of the hydrogen molecular ion, the time averaged internuclear distance is increased by the zero order molecular vibration A 07% increase in the semimajor axis and the reciprocal decrease in the semiminor axis releases energy which is equal to one half the vibrational energy Substitution of a = 1007 a© and b = 0702 ao into Eqs (214-221) with the reduction of the total energy by one half the vibrational energy is E vl ED = E ( 2 H[ a 0 ] ) - Eτ ze ro order " 2 = _27 ' 2 1 + 3 1 ' 94 = 4 73 eV ( 222 Eq (222) is the bond dissociation energy where E vl is given by Eq (223) The experimental value i s - 75 eV Substitution of a = 1 005 ao into Eq E vi b = 0 582 eV (223 The experimental value is 0 55 eV which is calculated using the quantum harmonic osci llator approximation with the experimental value of the first vibrational transition. + THE DIHYDRINO MOLECULAR ION H* 2 [ 2 C = a 0 ] Force balance between the electric and centripetal forces is given by Eq. ( 133) where p = 2 h 2 2e 2 2ab2 X = X (224 m e a 2 b 2 ~ 4πεo which has the parametric solution given by Eq. ( 127) when a = a 0 . (225 The semimajor axis, a, is also given by Eq. ( 134) where p = 2. The internuclear distance, 2c', which is the distance between the foci is given by Eq. ( 143) where p = 2. 2C = a 0 (226 The semiminor a The eccentricity, e, is given by Eq. ( 147). 1 e = ( 228) Energies of the Dihydrino Molecular I on H*2[2C = a 0 ] The potential energy, V e , of the electron M. 0 in the field of magnitude twice that of the protons at the foci (ξ = 0) is given by Eq ( 135) where p = 2 -8e 2 a + a - b 2 V e = , In / (229) 8πε 0 / a 2 - b 2 a - a 2 - b 2 The potential energy, Vp, due to proton-proton repulsion in the field of magnitude twice that of the protons at the foci (ξ = 0) is given by Eq M48) where p = 2 The kinetic energy, T, of the electron M 0 is given by Eq (137) where p = 2 2h 2 , a + a 2 - b 2 T = . in , (231) m e aV a 2 - b 2 a - a 2 - b 2 Substitution of a and b given by Eqs (225) and (227), respectively, into Eqs. (229), (230), and (231) is -16e 2 V e = In 3 = -239058 eV (232) oπεoao T = 0 8β In 3 = 119.53 eV (234) δπεoao ET = V e + V p + T (236) ET = 13.6eV ( -161n3 + 4 + 61n3 ) = -65.09 eV (237) The bond dissociation energy, ED, IS the difference between the binding energy of the corresponding hydrino atom and ET ED = E( Hyj ) - ET = 10.69 eV (23δ) Eqs (232-23δ) are equivalent to Eqs (149-154) where p = 2 Vibration It can be shown that a perturbation of the orbit determined by an inverse square force results in simple harmonic oscillatory motion of the orbit Zero order vibration arises because the state is nonradiative and is an energy minimum The time average internuclear distance is increased by the zero order vibration A 015% increase in the semimajor axis and the reciprocal decrease in the semiminor axis decreases ET by the vibrational energy and releases energy equal to one half the vibrational energy Substitution of a = 10015 ao and b = 08647 ao into 72 Eqs (229). (230), (231), and (236) and (238) with the reduction of the total energy by one half the vibrational energy is E vιb ED = E ( H 2 ) - Eτ zero ordei -544 + 6539 09? .(23 Eq (239) is the bond dissociation energy where E V)b is given by Eq (240 Substitution of a = 10015 ao into Eq (165) is E vlb = 0588 eV (24 THE DIHYDRINO MOLECULE H*2 2C = 5 Force Balance The force balance equation for the dihydrino molecule H*2 l" is given by Eq. (175) where p = 2 h 2 2e2 h "2 χ (241 m e a b 2 2ab2 χ " = l 4^πεo X + 2 ^'"e* ab2 which has the parametric solution given by Eq. (127) when ao a = 2- (24 The semimajor axis, a, is also given by Eq. (177) where p = 2. The internuclear distance, 2C, which is the distance between the foci is given by Eq (178) where p = 2. 2c ' = V* a 0 (243 The semiminor axis is given by Eq. (179) where p = 2. "c Xll 30 (244 The eccentricity, e, is given by Eq (180) 1 e" X (245 Energies of the Dihydrino Molecule HH2C = The energies of the dihydrino molecule H*2 2c " = are given X by Eqs (181-187) where p = 2 73 The energy, V , of the magnetic force is Vm = -67.8069 eV (24 ET = V e + T + Vm + V p (25 ET φ xL - <*].- 126.5 eV (25 E( 2 H ) = -2(54.4) eV (25 The bond dissociation energy, ED, is the difference between the binding energy of the corresponding hydrino atoms and ET- ED = E( 2 ®'- ET = 17.68δ eV (25 As in the case of the dihydrino molecular ion, the time averaged internuclear distance is increased by the zero order molecular vibration A 0.7% increase in the semimajor axis and the reciprocal decrease in th sem iminor axis releases energy which is equal to one half the vibrational energy Substitution of a = 0.5035 ao and b = 0.351 ao into Eqs (246-253) with the reduction of the total energy by one half the vibrat ional energy is E vit ED = E( 2 H] ■ £ ) " ET; zero order 2 = - 108.8 + 127.66 = 18.86 eV (25 Eq (254) is the bond dissociation energy where E V] is given by Eq (255) Substitut ion of a = 0 5035 ao into Eq ( 165) is E vl b = 2.33 eV (25 Ionization Energies The first ionization energy, I P ] , of the dihydrino molecule H 2c " = H^2[ 2 ( = a r (256 is given by Eqs (236) and (250) w ith zero order vibration, Eαs (239) and (254), respectively I P i = (257 I i = -6539 eV + 12766 eV = 62 27 eV (258 The second ionization energy, I P2, is given by Eq (236) with zero order vibration, Eq (239) IP2 = 65.39 eV (259 A hydnno atom can react with a hydrogen, deuterium, or tritium nucleus to form a hydnno molecular ion that further reacts with an electron to The energy ed is E = E( #] > - ET (261 ) where ET is given by Eq. (250) with zero order vibration, Eq (254). A hydrino atom can react with a hydrogen, deuterium, or tritium atom to form a dihydrino molecule. The energy released is E = E( H ) + E( H[a 0 ] ) - ET (263) I P where ET is given by Eq (250) with zero order vibration, Eq (254) Below "Ground State" Transitions of Hvdrooen-Tvpe Molecules and Molecular Ions Excited states of orbitspheres are discussed in the Excited States of the One Electron Atom (Quantization) Section of The Unif ication of Spacetime. the Forces. Matter, and Energy. Mil ls, R , Technomics Publishing Company, Lancaster, PA, ( 1 992) In the case of ellipsoidal M 0 's, exci ted electronic states are created when photons of discrete 9873 75 frequencies are trapped in the el lipsoidal resonator cavity of the M 0 The photon changes the effective charge at the M 0 surface where the central field is el lipsoidal and arises from the protons and the effectiv charge of the trapped photon at the foci of the M 0 Force balance is achieved at a series of ellipsoidal equipotential two dimensional surfaces confocal with the ground state ell ipsoid The trapped photons are solutions of the Laplacian in el lipsoidal coordinates, Eq. ( 103). As is the case with the orbitsphere, higher and lower energy stat are equally valid. The photon standing wave in both cases is a solution of the Laplacian in ellipsoidal coordinates. For an ellipsoidal resonator cavity, the relationship between an allowed circumference, 4aE, and th photon standing wavelength, λ, is 4aE = nλ (26 where n is an integer and where a 2 - b2 k = ~ a (26 is used in the elliptic integral E of Eq. (264). Applying Eqs. (264) and (265), the relationship between an allowed angular frequency given by Eq. ( 100) and the photon standing wave angular frequency, ω, is: rfi h h 1 m e A = m e naι nbι = m e a n b n = n 2 ωι = ω " (26 where n = 1 , 2, 3, 4, ... n 1 2 , 1 3 , 1 4 , ... eu, is the al lowed angular frequency for n = 1 a ] and b] are the allowed semimajor and semiminor axes for n = 1 ENERGY HOLES From Eq (266), the magnitude of the elliptic field corresponding t a below "ground state" transition of the hydrogen molecule is an integer. The potential energy equations of hydrogen-type molecules are Vv'here 76 ao (26 P and where p is an integer (These energies are approximate in that they do not include the energy component corresponding to zero order vibration. The exact energies are given by Eqs. (267-268) where the parameters a and b are those given by Eqs. (269-270) with the correctio for zero order vibration as given in the Vibration Section). From energy conservation, the resonance energy hole of a hydrogen-type molecule - which causes the transition H* (272 is mp 2 X 48.6 eV (273 where m and p are integers. During the transition, the elliptic field is increased from magnitude p to magnitude p + m. The corresponding potential energy change equals the energy absorbed by the energy hole. Energy hole = -V e " V p = mp 2 X 48.6 eV (274 Further energy is released by the hydrogen-type molecule as the internuclear distance " shrinks " . The total energy, ET, released during th transi tion is JjL -L - ( m + 13.6 ev[[2p 2 V2 - - p 2 2 (275 (This energy is approximate in that it does not include the energy component corresponding to zero order vibration. The exact energy is given by Eq. (275) with the correction for zero order vibration as given i the Vi brat ion Section) A schematic drawing of the total energy wel l of hydrogen-type molecules and molecular ions is given in FI GURE. 3. The exothermic reaction involving transitions from one potential energy level to a lower level is also hereaf ter referred to as HECTER (Hydrogen Emission by Catalyti c Thermal Electronic Relaxation) 77 A hydrogen-type molecule with its electrons in a lower than " ground state " energy level corresponding to a fractional quantum numb is hereaf ter referred to as a dihydrino molecule The designat ion for a dihydrino molecule of internuclear distance, 2c ' = where p is a A schematic drawing of the size of hydrogen-type molecules as a function of total energy is given in FIGUR 4. The magnitude of the ell iptic field corresponding to the first belo " ground state " transition of the hydrogen molecule is 2. From energy conservation, the resonance energy hole of a hydrogen molecule which excites the transition of the hydrogen molecule with internuclear distance 2c' = V~2 ao to the first below "ground state" with internuclear distance 2c " = -7= ao is given by Eqs. (267-271 ) where th ell iptic field is increased from magnitude one to magnitude two: -2e2 a + a 2 - D 2 V e = ~ , In , = -67.813 eV (276 δπεcr / a 2 - b 2 a - J a 2 - 2 = 19.23 eV (277 Vp = δπεo^ a 2 _ b 2 Energy hole = -V e - V p = 4δ.6 eV (278 In other words, the ell iptic " ground state" field of the hydrogen molecule can be considered as the superposition of Fourier components. The removal of negative Fourier components of energy m x 48.6 eV (279 where m is an integer, increases the positive electric field inside the el l ipsoidal shell by m times the charge of a proton at each focus The resultant electric field is a time harmonic solution of the Laplacian in el l ipsoidal coordinates The correspond ing potential energy change equals the energy absorbed by the energy hole Energy hole = -V e - Vp = m X 48 6 eV (280 Further energy is released by the hydrogen molecule as the internuclear distance " shrinks " The hydrogen molecul e with internuclear distance 2c = 2 a© is caused to undergo a transition to the a below " ground state level, and the internuc lear d istance for whi ch force ba lance and nonradiation are achieved is 2c ' In decaying to this internuclear distance from the " ground state " , a tota l energy of - 13 6 ev 2( 1 + m) 2 V2 - ( l + m ) 2 V2 - 1 l + m ) 2 V2 + 13.6 eV 2 2 - 2 (28 1 is released. In a preferred embodiment, energy holes, each of approximately m X 48.6 eV, are provided by electron transfer reactions of reactants including electrochemical reactant(s) (electrocatalytic couple(s)) which cause heat to be released from hydrogen molecules as their electrons ar stimulated to relax to quantized potential energy levels below that of the "ground state". The energy removed by an electron transfer reaction, energy hole, is resonant with the hydrogen energy released to stimulate this transition The source of hydrogen molecules is the production on the surface of a cathode during electrolysis of water in the case of an electrolytic energy reactor and hydrogen gas or a hydride in the case of a pressurized gas energy reactor or gas discharge energy reactor. CATALYTIC ENERGY HOLE STRUCTURES FOR MOLECULES Single Electron Transfer An energy hole is provided by the transfer of an electron between participating species including atoms, ions, molecules, and ionic and molecular compounds In one embodiment, the energy hole comprises the transfer of an electron from one species to another species whereby the sum of the ionization energy of the electron donating species m inus the ionizat ion energy or electron aff inity of the electron accepting species equals approximately mp 2 X 48 6 eV where m and p are integers Single Electron Transfer (Two Species) An eff i cient catalyt ic system that hinges " on the coupl ing of three resonator caviti es involves iron and l ith ium For example, the fourth ionization energy of iron is 548 eV This energy hole is obvi ously too 79 high for resonant absorption However, Lι + releases 5 392 eV when it i reduced to Li The combination of Fe 3 + to Fe 4 + and Lι + to Li, then, has net energy change of 49 4 eV 49 4 eV + Fe 5 + + Lι + + H 2 [2c " = yβ a 0 ] 2 a 0 - Fe« + + Li H- ^ 2 2c " = + 95 7 eV (28 Li + Fe 4+ → Li + + Fe 3 " + 49 4 eV (28 And, the overall reaction is y β ao H 2 [2c' = y β a 0 ] → H* 2 2c " = + 95.7 eV (28 Note that the energy given off as the molecule shrinks is much greater than the energy lost to the energy hole. And, the energy released is larg compared to conventional chemical reactions. An efficient catalytic system that hinges on the coupling of three resonator cavities involves scandium. For example, the fourth ionizatio energy of scandium is 73.47 eV. This energy hole is obviously too high for resonant absorption. However, Sc 3 + releases 24.76 eV when it is reduced to Sc 2 + . The combination of Sc 3 + to Sc 4+ and Sc 3 + to Sc 2+ , then, has a net energy change of 48.7 eV. 4δ.7 eV + Sc 3 + + Sc3 + + H 2 [2c' = yβ a 0 ] - Sc 4 + + Sc 2 + + H* 2 2C + 95.7 eV (285 Sc 2+ + Sc 4+ — Sc 3 + + Sc 3+ + 4δ.7 eV (286 And, the overall reaction is y β a 0 1 H 2 [2C = yβ a 0 ] - H* 2 2C = 95.7 eV (287 An efficient catalytic system that hinges on the coupling of three resonator cavities involves yttrium. For example, the fourth ionization energy of gal l ium is 64.00 eV This energy hole is obviously too high for resonant absorption However, Pb 2 + releases 1 5.03 eV when it is reduced to Pb + The combination of Ga 3 + to Ga 4 + and Pb 2 + to Pb + , then, has a net energy change of 48 97 eV 48 97 eV + Ga 3 + + Pb 2 + + H 2 [2C = y β a 0 ] yβ ao - Ga 4 + + Pb + + H^9: 2c " = + 95 7 eV (288 2 80 Ga 4 + + Pb + - Ga 3 + + Pb 2 (28 And, the overal l reaction is H 2 [2C = yβ a 0 ] - H 2 95 7 eV (29 Catalyti c systems that hinge on the transfer of one electron from an atom or ion to an atom or ion capable of producing energy holes for shrinking hydrogen molecules are given in the fol lowing table/ The number in the column following the ion, (n), is the nth ionization energy of the atom. That is for example, Ga 3+ + 64.00 eV = 6a 4+ + e ~ and H + + e " = H + 13.60 eV. 8; r-; 0 Mn 5 + 6 9500 Mo 4 + 4 4640 Mn 5 + 6 4860 9500 Lu 4 + 4 45 19 Mn 5+ 6 4981 9500 Bi 4 + 4 4530 Fe 3 + 3 4970 5480 Fe 1 + 787 Ni 3 + 3 4693 5490 Fe 1 + 787 Cu 3 + 3 4703 5520 Fe 1 + 787 Sr 3 + 3 4733 5700 Fe 1 + 787 Sb 4+ 4 4913 56.00 Fe 1 + 7.87 Bi 4 + 4 48.13 56.00 Fe 1 + 7.87 4813 Ga 3 + 3 64.00 Fe 2 + 2 16.18 As 4 + 4 47.82 63.63 Fe 2 + 2 6.18 Co 4 + 4 47.45 79.50 Fe 3 + 3 3065 Fe 3 + 4 48.85 54.80 Fe 1 + 7.87 Fe 3 + 4 46.93 54.80 Co 1 + 7.86 Fe 3 + 4 46.94 54.80 Ni 1 + 7.64 Fe 3 + 4 47.17 54.80 Cu 1 + 7.73 Fe 3 + 4 47.07 54.80 Ga 1 + 6.00 Fe 3 + 4 48.80 54.80 Ge 1 + 7.90 Fe 3 + 4 46.90 54.80 Sr 1 + 5.70 Fe 3 + 4 49.10 54.80 Y 1 + 6.38 Fe 3 + 4 48.42 54.80 Zr 1 + 6.84 Fe 3 + 4 47.96 54.80 Nb 1 + 6.88 47.92 Nb 5 + 5 102.60 Fe 4 + 54.80 Fe 3 + 4 47.80 54.80 Mo 1 + 7.10 Fe 3 + 4 47.70 54.80 Tc 1 + 7.28 Fe 3 + 4 47.52 54.80 Ru 1 + 7.37 Fe 3 + 4 47.43 5480 Rh 1 + 746 47.34 Fe 3 + 4 5480 Ag ι + 7.58 Fe 3 + 4 4722 5480 In 1 + 579 4901 Fe 3 + 4 5480 Sn 1 + 734 4746 Fe 3 + 4 5480 Ba 1 + 521 4959 Fe 3 + 4 5480 La 1 + 558 4922 Fe 3 + 4 5480 Ce 1 + 547 4933 Fe 3 + 4 5480 Pr 1 + 542 4938 Fe 3 + 4 5480 Nd 1 + 549 4931 Fe 3 + 4 5480 Pm 555 4925 54 90 Zr 1 + 6 84 48 06 54 90 Nb 1 + 6.88 48.02 1 02 60 Ni 4 + 54 90 47 70 54 90 Mo 1 + 7 1 0 47.80 54.90 Tc 1 + 7.28 47 62 54.90 Ru 1 + 7 37 47 53 54 90 Rh 1 + 7.46 47.44 54.90 Ag ι + 7.58 47.32 54.90 In 1 + 5.79 49. 1 1 1 0 54.90 Sn 1 + 7.34 47.56 54.90 Ba 1 + 5.21 49.69 54.90 La 1 + 5.58 49.32 54.90 Ce 1 + 5.47 49.43 54.90 Pr 1 + 5.42 49.48 1 5 54.90 Nd 1 + 5.49 49.41 54.90 Pm 1 + 5.55 49.35 54.90 Sm 1 + 5.63 49.27 54.90 Eu 1 + 5.67 49.23 54.90 Gd 1 + 6. 14 48.76 20 54.90 Tb 1 + 5.85 49.05 54.90 Dy 1 + 5.93 48.97 54.90 Ho 1 + 6.02 48.88 54.90 Er 1 + 6. 10 48.80 54.90 Tm I + 6. 18 48.72 25 54.90 Yb 1 + 6.25 48.65 54.90 Lu 1 + 5.43 49.47 54.90 Hf 1 + 6.60 48.30 54.90 Ta 1 + 7.89 47.0 1 54.90 W 1 + 7.98 46.92 30 54 90 Re 1 + 7.88 47.02 54.90 Tl 1 + 6 1 1 48.79 54 90 Pb 1 + 7.42 47.48 54 90 Bi 1 + 7.29 47.6 1 54 90 Ra 1 + 5.28 49.62 35 54.90 Ac 1 + 5.20 49.70 54 90 Th 1 + 6 10 48.80 0 4836 4799 4700 4762 4962 4962 49.56 48.96 4748 50.18 49.56 48.67 47.48 47.17 50.56 49.71 50.28 50.13 50.00 <49.87 49.75 49.62 47.90 46.90 46.77 49.84 47.46 48.53 4897 4904 4717 4716 4916 4916 4807 4929 UJ UJ to to cn o ui o Ul Ul ^. 3. ^ ^ m^. 3 3 3 3 3 3 3 3 3 3 3 3 3 C0 CD C0 - Z 0D U ) 3 CD Ul - N N N N N N H o o o o o o o o o o o o o o o o o o cr — T -' CT — --l O — • cr ^3 — j — » — j — j Φ cn n A A A A A A A A A A A A A A A ^ -^ A Ul A <-" A A ■ A W A A A A A A cn + + + + + + + + + + + + + + + + cn CT m ui cn n n cn Ul Ul Ul Ul Ul Ul Ul Ul Ul Ul UI A A UJ Ul UI A A A A UJ Ul Ul Ul tJi n A Ul oi CT cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn — uι uι uι uι oo si cn uι uι uι co oo co <.-o oo oo sj co co — — — — — — — — — — — — — — — — o p p A O p to — cn cn A — — — — — — o o o ro ro ro ro ro ro ro ro ro fo fo ro io to to ro CO o o o o o o o o o o o o o o o o o o b b o bo bo ϋcni uo rooo roo bo oo bo coπ coπ con uo i uo i o sj o o ro χ X TJ TJ rsi ISI o τj- χr i3 rC- c-r H m-5 χo -<σ CHT CT m co τ z n r- χ :∑ 3 3 3 θ Q. c ^ 3 Q. z z φ ή) Φ o θ O θ ) cr c z c zr z cr c zr cr g .,_. -. 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UJ UJ UI UI UI UI UJ UJ UJ UI UJ U1 UJ UJ UJ UI + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Ul Ui Ui A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A sj si oo ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui ui cn ui ui cn cπ cπ ui cπ cπ rO tO OO CT CT A A A A A A A A A A A A A A A A A A A A A A A A A A lo to ui o o o b b b b b b b b b b ό b b ό b b b b b b b b b o o o o o o b oo oo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o A O Uri ui cDn c/ji mω n— . ci-i ng > cT Zj C T cuj H rr > o : cXo7 0 —-i • H — — > ic — -σ< H:^ mτ o ^σ< cr Q Q- ~' ( τ ι ' c ro ui A — — — — — _ _ — — ~ ' — — — — -' —' — — — _ > ~ i — — — — — __ _ — — — — — + + + + + + + + + + + + 4- + + + + + + + + + + + + + + + + + + + + + + ro ui A — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — rO fO A sl sJ CT CT CT CT Ul CT CT CT Ul CT Ul Ul sJ CT CT Ul CT CT CT CT Ul Ul CT ^ ^ ° uι u A J ro b b r b — ro ro r — CT A r — — b b bo — n C T ui A Ui tό — uj sj A A ro o uι rθ Nθ CT θ uι o o o oθ Nθ — o uJ Ui oo o to ui ui A si uj ui o r si co — o o UJ A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A s j CT sj p p sj j j j s j s j s j p sl p sl si p sl s j si si p p sl p p ω — NO Ul CT CT Ul si si b b b co b — ID b si si ffl A Ul si bo b b O — bo uj UJ A Ui cπ ui A si co co sj CT CT cxi O sJ CD — A o ui o o o ro — NO O si ui ro o cD si ui cn uJ si ui — co r D 05 07 08 An energy hole is provided by the ionization of an electron from a participating species including an atom, an ion, a molecule, and an ionic or molecular compound to a vacuum energy level. In one embodiment, the energy hole comprises the ionization of an electron from one species to vacuum energy level whereby the ionization energy of the electron donating species eguals approximately mp 2 X 48.6 eV where m and p are integers. Catalytic systems that hinge on the transfer of one electron from an atom or ion to a vacuum energy level capable of producing energy holes for shrinking hydrogen molecules are given in the following table. The number following the atomic symbol (n) is the nth ionization energy of the atom. That is for example, Na + + 47.29 eV = Na 2+ + e " . Multiple Electron Transfer An energy hole is provided by the transfer of multiple electrons between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one or more species whereby the sum of the ionization energies and/or electron aff inities of the electron donating species minus the sum of the ionization energies and/or electron aff inities of the electron acceptor species eguals approximately mp 2 X 48.6 eV where m, p, and t are integers An energy hole is provided by the transfer of mult iDle el ectrons between part icipati ng species including atoms, ions, mol ecules, and ion ic and molecular compounds In one embodiment, the energy hole comprises the transfer of t e lect rons from one spec ies to another whereby the t consecut ive electron aff init ies and/or i onization energies of the el ectron donating spec ies minus the t consecutive i onization energies and/or electron af f initi es of the el ectron acceptor eguals approximately mp 2 X 48 6 eV where m, p, and t are integers In a preferred embodiment the electron acceptor species is an oxide such as MnOχ, A10χ, SiOχ. A preferred molecular electron acceptor is oxygen, O2. Two Electron Transfer (One Species) In an embodiment, a catalytic system that provides an energy hole hinges on the ionization of two electrons from an atom, ion, or molecule to a vacuum energy level such that the sum of two ionization energies is approximately mp 2 X 48.6 eV where m, and p are integers Two Electron Transfer (Two Soecies) In another embodiment, a catalytic system that provides an energy hole hinges on the transfer of two electrons from an atom, ion, or molecule to another atom or molecule such that the sum of two ionization energies minus the sum of two electron affinities of the participating atoms, ions, and/or molecules is approximately mp 2 X 48.6 eV where m and p are integers. Two Electron Transfer (Two Soecies) In another embodiment, a catalytic system that provides an energy hole hinges on the transfer of two electrons from an atom, ion, or molecule to another atom, ion, or molecule such that the sum of two ionizati on energi es minus the sum of one ionization energy and one electron affini ty of the part icipat ing atoms, ions, and/or molecules i s approximately mp 2 X 48 6 eV where m and p are integers Other Energy Holes 0 I n another embodiment, energy hol es, each of approximately m X 67.8 eV given by Eq. (276) -m x V eP - = - -mI I I X Λ = m x 67.8 13 eV (29 are provided by electron transfer reactions of reactants including electrochemi cal reactant(s) (electrocatalytic couple(s)) which cause heat to be released from hydrogen molecules as their electrons are stimulated to relax to quantized potential energy levels below that of the "ground state " . The energy removed by an electron transfer reaction energy hole, is resonant with the hydrogen energy released to stimulate this transition. The source of hydrogen molecules is the production on the surface of a cathode during electrolysis of water in the case of an electrolytic energy reactor and hydrogen gas or a hydride in the case of pressurized gas energy reactor or gas discharge energy reactor. An energy hole is provided by the transfer of one or more electron between participating species including atoms, ions, molecules, and ionic and molecular compounds. In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one o more species whereby the sum of the ionization energies and/or electro affinities of the electron donating species minus the sum of the ionization energies and/or electron affinities of the electron acceptor species equals approximately m x 67.8 eV where m and t are integers. An efficient catalytic system that hinges on the coupling of three resonator cavities involves magnesium. For example, the third ionization energy of magnesium is 80.143 eV. This energy hole is obviously too high for resonant absorption. However, Sr 2 + releases 1 1.03 eV when it is reduced to Sr + . The combination of Mg 2 + to Mg 3 + and Sr 2 + to Sr + , then, has a net energy change of 69. 1 eV. H 2 [2C = yβ a 0 ] ao H- Z ^ . 95 7 eV 2 (294) An effi cient catalyti c system that hi nges on the coupl i ng of three resonator cavities involves magnesium For exampl e, the third ionizati on energy of magnesium is 80 1 43 eV Thi s energy hole is obviously too high for resonant absorption However, Ca + rel eases 1 1.871 eV when it is reduced to Ca + The combination of l g + to Mg 5 + and Ca 2 + to Ca + , then, has a net energy change of 68.2 eV. - Mg3 + + Ca + + H* 2 2C= + 95.7 eV (295) Mg3 + + Ca + → Mg 2 + + Ca + + 68.2 eV (296) And, the overall reaction is 2 ao H 2 [2C = yβ a 0 ] - H* 2 2c" = 2 J + 95.7 eV (297) In four other embodiments, energy holes, each of approximately n x Ej eV given by Eq. (275) with zero order vibration and/or approximately n x ET eV given by Eq. (281 ) with zero order vibration and/or approximately m x 31.94 eV given by Eq. (222) and/or approximately 95.7 eV (corresponding to m = 1 in Eq. (281 ) with zero order vibration which is given by the difference in Ejzero order of Eqs. (254) and (222)) are provided by electron transfer reactions of reactants including electrochemical reactant(s) (electrocatalytic couple(s)) which cause heat to be released from hydrogen molecules as their electrons are stimulated to relax to quantized potential energy levels below that of the "ground state " . The energy removed by an electron transfer reaction, energy hole, is resonant w ith the hydrogen energy released to stimulate this transition. The source of hydrogen molecules is the production on the surface of a cathode during electrolysis of water in the case of an electrolytic energy reactor and hydrogen gas or a hydride in the case of a pressurized gas energy reactor or gas discharge energy reactor An energy hole i s provided by the transfer of one or more electrons between part icipating species including atoms, ions, mol ecules, and ionic and molecular compounds In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one or more species whereby the sum of the ioni zati on energies and/or electron af f ini t i es of the electron donating species minus the sum of the ionizat ion energies and/or electron aff init ies of the electron acceptor species equals approximately m x 3 1 94 eV ( Eq (222)) where m and t are i nt egers An energy hole is provided by the transf er of one or more electrons between partici pating species including atoms, ions , molecules, and ionic and molecular compounds In one embodiment, the energy hole comprises the transfer of t electrons from one or more species to one or more species whereby the sum of the ionization energies and/or electron aff inities of the electron donating species minus the sum of the ionization energies and/or electron aff inities of the electron acceptor species equals approximately m X 95.7 eV where m and t are integers ' . ENERGY REACTOR An energy reactor 50, in accordance with the invention, is shown in FIGURE 5 and comprises a vessel 52 which contains an energy reaction mixture 54, a heat exchanger 60, and a steam generator 62. The heat exchanger 60 absorbs heat released by the shrinkage reaction, when the reaction m ixture, comprised of shrinkable material, shrinks. The heat exchanger exchanges heat with the steam generator 62 which absorbs heat from the exchanger 60 and produces steam. The energy reactor 50 further comprises a turbine 70 which receives steam from the steam generator 62 and supplies mechanical power to a power generator 80 which converts the steam energy into electrical energy, which is received by a load 90 to produce work or for dissipation. The energy reaction mixture 54 comprises an energy releasing material 56 including a source of hydrogen i sotope atoms or a source of molecular hydrogen isotope, and a source of energy holes 58 which resonantly remove approximately m X 27.21 eV to cause atomic hydrogen " shrinkage" and approximately m X 48 6 eV to cause molecular hydrogen " shrinkage " where m is an integer The shrinkage reacti on releases heat and shrunken atoms and/or molecules The source of hydrogen can be hydrogen gas, electrolysis of water, hydrogen f rom hydrides, or hydrogen from metal-hydrogen solutions In al l embodiments, the source of energy holes is one or more of an el ectrochemical , chemica l , photochem ical, thermal , free radical, some, or nuc lear ractιon ( s) or inel astic photon or partic le scattering reactιon(s) I n the latter two cases, the present invention of an energy reactor comprises a particle source 75b and/or photon source 75a to supply the said energy holes I n these cases, the energy hole corresponds to stimul ated emissi on by the photon or part icle In a pret erred embodiments of the pressurized gas energy and gas d ischarge reactors shown in FI GURES 7 and 8, respect ively, a photon source 75a dissociates hydrogen molecules to hydrogen atoms. The photon source producing photons of at least one energy of approximately n X 27.21 eV, n/2 X 27.21 eV, or 40.8 eV causes stimulated emission of energy as the hydrogen atoms undergo the shrinkage reaction. In another preferred embodiment, a photon source 75a producing photons of at least one energy of approximately n X 48.6 eV, 95.7 eV, or n x 31.94 eV causes stimulated emission of energy as the hydrogen molecules undergo the shrinkage reaction. I n all reaction mixtures, a selected external energy device 75, such as an electrode may be used to supply an electrostatic potential or a current to decrease the activation energy of the resonant absorption of an energy hole. In another embodiment, the mixture 54, further comprises a surface or material to absorb atoms and/or molecules of the energy releasing material 56. Such surfaces or materials to absorb hydrogen, deuterium, or tritium comprise transition elements and inner transition elements including iron, platinum, pal ladium, zirconium, vanadium, nickel, titanium, Sc, Cr, Mn, Co, Cu, Zn, Y, Nb, Mo, Tc, Ru, Rh, Ag, Cd, La, Hf, Ta, W, Re, Os, lr, Au, Hg, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Oy, Ho, Er, Tm, Yb, Lu, Th, Pa, and U. In a preferred embodiment, a source of energy holes to shrink hydrogen atoms comprises a catalytic energy hole material 58, typical ly comprising electrochem ical couples including the catalytic couples described in my previous U.S. patent appl ication entitled "Energy/ Matter Conversion Methods and Structures, " fi led on April 28, 1989 which is incorporated by reference. In a preferred embodiment, a source of energy holes to shrink hydrogen molecules comprises a catalyti c energy hole material 58, typical ly compri sing electrochem ical couples inc luding the catalyt ic couples that provide an energy hole of approximately m x 48 6 plus or m inus 5 eV. A further embodiment is the vessel 52 containing a molten, liquid, or sol id solution of the cata lyt ic couple(s) and a source of hydrogen inc luding hydrides and gaseous hydrogen In the case of a reactor which shr inks hydrogen atoms, the embodiment f urther comprises a means to dissociate the molecular hydrogen into atomic hydrogen including the transi tion or inner transition metals or electromagnetic radiation including UV l ight provided by photon source 75 The present invention of an electrolytic cel l energy reactor, pressurized gas energy reactor, and a gas discharge energy reactor, comprises: a means for containing a source of hydrogen; a means for bringing the hydrogen atoms (molecules) into contact with one of a solid molten, liquid, or gaseous solution of energy holes; and a means for removing the lower-energy hydrogen atoms (molecules) so as to prevent an exothermic shrinkage reaction from coming to equilibrium. The present energy invention is further described in my previous U.S. Patent Applications entitled "Energy/ Matter Conversion Methods and Structures," filed on April 28, 1989, December 12, 1990, and June 1 1 , 1993 and my publication, Mills, R., Kneizys, S., Fusion Technology., 210, ( 1991 ), pp. 65-81 which are incorporated herein by reference. Electrolytic Energy Reactor An electrolytic energy reactor is described in my previous U.S. Patent Appl ications entitled "Energy/ Matter Conversion Methods and Structures," filed on June 1 1 , 1993, December 1 2, 1990, and April 28, 1989 which are incorporated herein by reference. A preferred embodiment of the energy reactor of the present invention comprises an electrolyic cell forming the reaction vessel 52 of FIGURE 5 including a molten electrolytic cell. The electrolytic cel l 100 is shown generally in FIGURE 6. An electric current is passed through the electrolytic solution 102 having an electrocatalytic couple providing energy holes equal to the resonance shrinkage energy ( including the catalytic couples described in my previous U.S Patent Application entitled " Energy/ Matter Conversion Methods and Structures, " fi led on April 28, 1989 which is incorporated by reference) by the application of a voltage to an anode 104 and cathode 106 by the power controller 108 powered by the power supply 1 10. Ultrasonic or mechanical energy may also be imparted to the cathode 106 and electrolytic solution 102 by vibrating means 1 1 2 Heat is suppl ied to the electrolyt ic solution 102 by heater 1 14 The pressure of the - electrolytic cel l 100 is control led by pressure regulator means 1 1 6 where the cel l is closed The reactor further comprises a means 101 that removes the lower-energy hydrogen such as a selective venting valve to prevent the e - othermic shrinkage reaction from corn ing to equi l ibrium In a preferred embodiment, the electrolytic cell is operated at zer voltage gap by applying an overpressure of hydrogen with hydrogen source 121 where the overpressure is controlled by pressure control means 122 and 1 1 6 Water is reduced to hydrogen and hydroxide at the cathode 106, and the hydrogen is oxidized to protons at the anode 104. An embodiment of the electrolytic cell energy reactor, comprises reverse fuel cell geometry which removes the lower-energy hydrogen under vacuum. A preferred cathode 106 of this embodiment has a modified gas diffusion layer and comprises a gas route means including first Teflon membrane filter and a second carbon paper/Teflon membran filter composite layer. A further embodiment comprises a reaction vessel that is closed except for a connection to a condensor 140 on the top of the vessel 100. The cell is operated at a boil such that the steam evolving from the boiling electrolyte 102 is condensed in the condensor 140, and the condensed water is returned to the vessel 100. The lower- energy state hydrogen is vented though the top of the condensor 140. In one embodiment, the condensor contains a hydrogen/oxygen recombiner 145 that contacts the evolving electrolytic gases. The hydrogen and oxygen are recombined, and the resulting water is returned to the vessel 100. The heat released from the exothermic reaction whereby the electrons of the electrolytically produced .hydrogen atoms (molecules) are induced to undergo transitions to energy levels below the "ground state" and the heat released due to the recombination of the electrolytical ly generated normal hydrogen and oxygen is removed by a heat exchanger 60 of FI GURE 5 which is connected to the condensor 140 In vacuum, in the absence of external fields, the energy hole to stimulate a hydrogen atom (molecule) to undergo a shrinkage transit ion is n X 27.21 eV (n X 48 6) where n is an integer This resonance shrinkage energy is altered when the atom (molecule) is in a media different from vacuum An example is a hydrogen atom (molecule) absorbed to the cathode 106 present in the aqueous electrolyt ic solution 1 02 having an appl ied electric fi eld and an intrins ic or appl ied magneti c f ie ld provided by external magnet ic f ield generator 75 Under these condi tions the energy hole required is sl i ghtly different from n X 27 2 1 eV (n X 48 6; Thus, a source of energy holes inc luding electrocata lyt ic couple reactants is selected which has a redox energy resonant w i th the resonance shrinkage energy when operat ing under these conditions In the case where a nickel cathode 1 06 is used to electrolyze an aqueous solution 102 where the cel l is operating within a voltage range of 1 4 to 5 volts, the K+/K+ and Rb+ (Fe 3+ /Lι + and Sc 3 + /Sc 3 + ) couples are preferred embodiments to shrink hydrogen atoms (molecules). The cathode provides hydrogen atoms (molecules), and the shrinkage reaction occurs at the surface of the cathode where hydrogen atoms (molecules) and the electrocatalytic couple are in contact. Thus, the shrinkage reaction is dependent on the surface area of the cathode. For a constant current density, giving a constant concentration of hydrogen atoms (molecules) per unit area, an increase in surface area increases the reactants available to undergo the shrinkage reaction. Also, an increase in cathode surface area decreases the resistance of the electrolytic cell which improves the electrolysis efficiency. A preferred cathode of the electrolytic cel l including a nickel cathode has the properties of a high surface area, a highly stressed and hardened surface such as a cold drawn or cold worked surface, and a large number of grain boundaries. In a preferred embodiment of the electrolytic cel l energy reactor, the source of energy holes is incorporated into the cathode, mechanically by methods including cold working the source of energy holes into the surface of the cathode; thermally by methods including melting the source of energy holes into the surface of the cathode and evaporation of a solvent of a solution of the source of energy holes in contact with the surface of the cathode, and electrostatical ly by methods including el ectrolyt ic deposition, ion bombardment, and vacuum deposition The shrinkage react ion rate is dependent upon the composition of the cathode 106. Hydrogen atoms (molecules) are reactants to produce energy via the shrinkage reaction Thus, the cathode must eff iciently provide a high concentration of hydrogen atoms (molecules) The cathode 106 i s comprised of any conductor or semiconductor including transition elements and compounds, actimde and lanthamde el ements and compounds, and group 1 MB and I VB elements and compounds Transition metals dissoc iate hydrogen gas into atoms to a more or lesser extent depending on the metal Nickel and titanium readi ly dissoc iate hydrogen molecules and are preferred embodiments for shrinking hydrogen atoms The cathode can alter the energy of the absorbed hydrogen atoms (molecules) and affect the energy of the shrinkage reaction A cathode material is selected which provides resonance between the energy hole and the resonance shrinkage energy In the case of the K+/K+ couple with carbonate as the counterion for catalyzing the shrinkage of hydrogen atoms, the relationship of the cathode material to the reaction rate is: Pt < Pd « Ti, Fe < Ni This is the opposite order of the energy released when these materials absorb hydrogen atoms. Thus, for this couple, the reaction rate is increased by using a cathode which weakly absorbs the hydrogen atoms with little perturbation of their electronic energies. Also, coupling of resonator cavities and enhancement of the transfer of energy between them is increased when the media is a nonlinear media such as a magnetized ferromagnetic media Thus, when a paramagnetic or ferromagnetic cathode is used, the cathode increases the reaction rate (coupling of the hydrogen and electrocatalytic couple, energy hole, resonator cavities) by providing a nonlinear magnetized media. Alternatively, a magnetic field is applied with the magnetic field generator 75 Magnetic fields at the cathode alter the energy of absorbed hydrogen and concomitantly alter the energy which effects shrinkage Magnetic fields also perturb the energy of the electrocatalytic reactions by altering the energy levels of the electrons involved in the reactions The magnetic properties of the cathode are selected as well as the strength of the magnetic f ield which is applied by magnetic field generator 75 to optimize shrinkage reaction rate-the power output A preferred ferromagnetic cathode is nickel A preferred method to clean the cathode of the electrolytic cel l including a nickel cathode is to anodize the cathode in a basic electrolytic solution including approximately 0 57 M X2CO3 (X is the alkali cation of the electrolyte including K) and to immerse the cathode in a dilute solution of H2O2 In a further embodiment of the cleaning 1 1 8 method, cyc l ic voltametry ith a second electrode of the same materia as the f irst cathode is peri ormed The cathode is then thoroughly rinse with disti l led water Organic material on the surface of the cathode inh ibits the catalyt ic react ion v. hereby the electrons of the el ectro lyt ical ly produced hydrogen atoms (molecules) are induced to undergo transitions to energy levels below the " ground state " Cleani ng by this method removes the organic material from the cathode surface and adds oxygen atoms onto the cathode surface. Doping the metal surface, including a nickel surface, with oxygen atoms by anodizing the cathode and cleaning the cathode in H2O2 greatly increases the power output by decreasing the bond energy between the metal and the hydrog atoms (molecules) which conforms the resonance shrinkage energy of- t absorbed hydrogen to the energy hole provided by the electrocatalytic couple including the K + / + (Sc 3 + /Sc 3 + ) couple. Different anode materials have different overpotentials for the oxidation of water, which can affect ohmic losses. An anode of low overpotential will increase the efficiency. Nickel, platinum, and dimensionally stable anodes including platinized titantium are preferre anodes. In the case of the K+/K+ electrocatalytic couple where carbonate is used as the counterion, nickel is a preferred anode. Nickel is also a preferred anode for use in basic solutions with a nickel cathod Nickel is inexpensive relative to platinum and fresh nickel is electroplated onto the cathode during electrolysis. A preferred method to clean a dimensional ly stable anode includin a platinized titanium anode is to place the anode in approximately 3 M HCI for approximately 5 minutes and then to rinse it with disti lled water. In the case of hydrogen shrinkage, hydrogen atoms at the surface o the cathode 1 06 form hydrogen gas which can form bubbles on the surface of the cathode. These bubbles act as an boundary layer between the hydrogen atoms and the electrocatalytic couple The boundary can be amel iorated by vibrating the cathode and/or the electrolytic solution 1 02 or by applying ul trasound with vibrating means 1 12, and by adding wetting agents to the electrolyt i c solution 1 02 -to reduce the surface tension of the water and prevent bubble formation The use of a cathode having a smooth surface or a wire cathode Drevents gas adherence. And an intermittent current, prov/ided by an on-off circui t of power control ler 108 provides periodic replenishing of hydrogen atoms which are di ssipated by hydrogen gas format ion fol lowed by diffusion into the soluti on whi le prevent ing excessive hydrogen gas format ion which could form a boundary layer The shrinkage reaction is temperature dependent Most chemical reactions double their rates for each 10 °C rise in temperature. Increasing temperature increases the col lision rate between the hydrogen atoms (molecules) and the electrocatalytic couple which will increase the shrinkage reaction rate. With large temperature excursions from room temperature, the kinetic energy distribution of the reactants can be sufficiently altered to cause the energy hgole and the resonance shrinkage energy to conform to a more or lesser extent. The rate is proportional to the extent of conformation or resonance of these energies. The temperature is adjusted to optimize the shrinkage reaction rate-energy production rate. In the case of the K+/K+ electrocatalytic couple, a preferred embodiment is to run the reaction at a temperature above room temperature by applying heat with heater 1 14. The shrinkage reaction is dependent on the current density. An increase in current density is equivalent, in some aspects, to an increase in temperature. The col lision rate increases and the energy of the reactants increases with current density. Thus, the rate can be increased by increasing the collision rate of the reactants; however, the rate may be increased or decreased depending on the effect of the increased reactant energies on the conformation of the energy hole and the resonance shrinkage energy. Also, increased current dissipates more energy by ohmic heating and may cause hydrogen bubble formation, in the case of the shrinkage of hydrogen atoms. But, a high flow of gas may dislodge bubbles which diminishes any hydrogen gas boundary layer. The current density is adjusted with power controller 108 to optimize the excess energy production In a preferred embodiment, the current density is in the range 1 to 1000 mil l iamps per square centimeter The pH of the aqueous electrolytic solution 102 can affect the shrinkage reaction rate I n the case that the electrocatalytic couple is positively charged, an increase in the pH wi l l reduce the concentration of hydroniυm at the negative cathode, thus, the concentration of the electrocata lyt ic couple cat ions wi l l increase An increase in reactant concentration increases the reaction rate. I n the case of the K+/K+ or Rb+ (Sc 3 + /Sc 3 + ) couple, a preferred pH is basic The counterion of the e lectrocatalyti c couple ot the electrolyt ic sol ution 102 can affect the shrinkage reaction rate by altering the energy of the transit ion state For example, the trans ition state comple of the K + /K + electrocata lytic couple w ith the hydrogen atom has a plus two charge and involves a three body collision which is unfavorable. A negative two charged oxyanion can bind the two potassiums; thus, it provides a neutral transition state complex of lower energy, whose formation depends on a binary col lision which is greatly favored. The rate is dependent on the separation distance of the potassium ions as part of the complex with the oxyanion. The greater the separation distance, the less favorable is the transfer of an electron between them. A close juxtaposition of the potassium ions will increase the rate. The relationship of the reaction rate to the counterion in the case where the K+/K+ couple is used is : OH " < P0 4 3 " , HP0 4 2 " < S0 4 2-« CO 3 2 - Thus, a planar negative two charged oxyanion including carbonate with at least two binding sites for K+ which provides close juxtaposition of the K+ ions is preferred as the counterion of the K+/K+ electrocatalytic couple. The carbonate counterion is also a preferred counterion for the Rb+ couple. A power controller 108 comprising an intermittent current, on-off, electrolysis circuit will increase the excess heat by providing optimization of the electric field as a function of time which provides maximum conformation of reactant energies, provides an optimal concentration of hydrogen atoms (molecules) while m inimizing ohmic and electrolysis power losses and, in the case of the shrinkage of hydrogen atoms, m inimizes the formation of a hydrogen gas boundary layer The frequency, duty cycle, peak voltage, step waveform, peak current, and offset voltage are adjusted to achieve the optimal shrinkage reaction rate and shrinkage reaction power whi le minimizing ohm ic and electrolysis power losses In the case where the K+/K+ electrocatalytic couple is used with carbonate as the counterion; nickel as the cathode; and platinum as the anode, a preferred embodiment is to use an interm ittent square-wave having an offset voltage of approximately 1 4 volts to 2 2 volts, a peak voltage of approximately 1 5 volts to 3 75 volts, a peak current of approximately 1 mA to 100 mA per square centimeter of cathode surface area, approximately a 5%-90% duty cycle, and a frequency in the range of 1 Hz to 1500 Hz Further energy can be released by repeating the shrinkage reaction The atoms (molecules) which have undergone shrinkage diffuse into the cathode lattice. A cathode 106 is used which will facil itates multiple shrinkage reactions of hydrogen atoms (molecules). One embodiment is to use a cathode which is fissured and porous to the electrocatalytic couple such that it can contact shrunken atoms (molecules) which have diffused into a lattice, including a metal lattice. A further embodiment is to use a cathode of alternating layers of a material which provides hydrogen atoms (molecules) during electrolysis including a transition metal and an electrocatalytic couple such that shrunken hydrogen atoms (molecules) periodically or repetitively diffuse into contact with the electrocatalytic couple. The shrinkage reaction is dependent on the dielectric constant of the media. The dielectric constant of the media alters the electric field at the cathode and concomitantly alters the energy of the reactants Solvents of different dielectric constants have different solvation energies, and the dielectric constant of the solvent can also lower the overpotential for electrolysis and improve electrolysis efficiency. A solvent, including water, is selected for the electrolytic solution 102 which optimizes the conformation of the energy hole and resonance shrinkage energy and maximizes the efficiency of electrolysis. The solubility of hydrogen in the reaction solution is directly proportional to the pressure of hydrogen above the solution Increasing the pressure increases the concentration of reactant hydrogen atoms (molecules) at the cathode 106 and thereby increases the rate But, in the case of the shrinkage of hydrogen atoms this also favors the development of a hydrogen gas boundary layer The hydrogen pressure is control led by pressure regulator means 1 16 to optimize the shrinkage reaction rate The heat output is moni tored with thermocouples present in at least the vessel 100 and the condensor 1 40 of FIGURE 6 and the heat exchanger 60 of Figure 5 The output power is control led by a computerized monitoring and control system which moni tors the thermistors and controls the means to alter the power output. Pressurized Gas Energy Reactor A pressurized gas energy reactor comprises the f irst vessel 200 of FIGURE 7 containing a source of hydrogen including hydrogen from metal- hydrogen solutions, hydrogen from hydrides, hydrogen from the electrolysis of water, or hydrogen gas. In the case of a reactor which shrinks hydrogen atoms, the reactor further comprises a means to dissociate the molecular hydrogen into atomic hydrogen such as a dissociating material including transition elements and inner transition elements including iron, platinum, palladium, zirconium, vanadium, nickel, titanium, Sc, Cr, Mn, Co, Cu, Zn, Y, Nb, Mo, Tc, Ru, Rh, Ag, Cd, La, Hf, Ta, W, Re, Os, lr, Au, Hg, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Oy, Ho, Er, Tm, Yb, Lu, Th, Pa, and U or electromagnetic radiation including UV light provided by photon source 205 such that the dissociated hydrogen atoms (molecules) contact a molten, liquid, or solid solution of the energy holes (including the catalytic couples described in my previous U.S. Patent Application entitled "Energy/ Matter Conversion Methods and Structures," filed on April 28, 1989 which is incorporated by reference). The pressurized gas energy reactor further comprises a means 201 to remove the lower-energy hydrogen such as a selective venting valve to prevent the exothermic shrinkage reaction from coming to equilibrium. One embodiment comprises heat pipes as heat exchanger 60 of FIGURE 5 which have a lower-energy hydrogen venting valve at a cold spot. A preferred embodiment of the pressurized gas energy reactor of the present invention comprises a first reaction vessel 200 with inner surface 240 comprised of a material to dissociate the molecular hydrogen into atomic hydrogen including the transition or inner transition metals The first reaction vessel 200 is sealed in a second reaction vessel 220 and receives hydrogen from source 221 under pressure which is controlled by pressure control means 222 The wall 250 of the f irst vessel 200 is permeable to hydrogen The outer wall 245 and/or outer vessel 220 has a source of energy holes equal to the resonance shrinkage energy In one embodiment the source of energy hol es is a soluti on containi ng energy holes in the molten, l iqui d, or so l id state In another embodiment an electric current i s passed through the material having a source of energy holes The reactor further comprises a means to control the reaction rate such as current source 225 and heating means 230 which heat the f irst reaction vesse l 200 and the second react ion vessel 220 I n a preferred embodiment the outer react ion vessel 220 contains oxygen, the inner surface 240 comprises one or more of a coat of nickel, platinum, or pal ladium. The outer surface 245 i s coated with one or more of copper, tel lurium, arsenic, cesium, platinum, or pal ladium and an oxide such as CuOχ, PtOχ, Pd0χ, Mn0χ, A10χ, SiOχ. The electrocatalytic couple is regenerated spontaneously or via a regeneration means including heating means 230 and current source 225. In another embodiment, the pressurized gas energy reactor comprises only a single reaction vessel 200 with a hydrogen impermeable wal l 250. I n the case of a reactor which shrinks hydrogen atoms, one or more of a hydrogen dissociating materials including the transition and inner transition elements are coated on the inner surface 240 with a source of energy holes including one or more of copper, tel lurium, arsenic, cesium, platinum, or palladium and an oxide such as Cu0χ, Pt0χ, Pd0χ, Mn0χ, A10χ, Si0χ. In another embodiment, the source of energy hole is one of a inelastic photon or particle scattering reaction(s). I n a preferred embodiment the photon source 205 suppl ies the energy holes where the energy hole corresponds to stimulated emission by the photon. In the case of a reactor which shrinks hydrogen atoms the photon source 205 dissociates hydrogen molecules into hydrogen atoms. The photon source producing photons of at least one energy of approximately n X 27.21 eV, n/2 X 27.21 eV, or 40.8 eV causes stimulated emission of energy as the hydrogen atoms undergo the shrinkage reaction In another preferred embodiment, a photon source 205 producing photons of at least one energy of approximately n X 48 6 eV, 95 7 eV, or n x 3 1 94 eV causes stimulated emission of energy as the hydrogen molecules undergo the shrinkage reaction A preferred i nner surface, 240, and outer surface, 245, of the pressurized gas energy reactor including a ni ckel surface has the properties of a high surface area, a highly stressed and hardened surface such as a co ld drawn or col d worked surface, and a large number of grain I n a preferred embodi ment or me pressurized gas energy reactor, the source of energy holes is incorporated into the inner surface, 240, and outer surf ace, 245, mechanical ly by methods i ncluding cold work ing the source of energy holes into the surface material, thermal ly by methods inc luding melting the source of energy holes into the surface material and. evaporation of a solution of the source of energy holes in contact w ith the surface material , and electrostatical ly by methods including electrolytic deposition, ion bombardment, and vacuum deposition. A preferred method to clean the inner surface 240 and the outer surface 245 including a nickel surface is to fill the inner vessel and the outer vessel with a basic electrolytic solution including approximately 0.57 M X2CO3 (X is the alkal i cation of the electrolyte including K) and to fill the inner vessel and the outer vessel with a dilute solution of H202. Each of the inner vessel and the outer vessel is then thoroughly rinsed with disti lled water. In one embodiment, at least one of the vessel 200 or the vessel 220 is then fi l led with a solution of the energy hole including an approximately 0.57 M K2CO3 solution. In one embodiment of the method of operation of the pressurized gas energy reactor, hydrogen is introduced inside of the first vessel from source 22 1 under pressure which is controlled by pressure control means 222. In the case of a reactor which shrinks hydrogen atoms, the molecular hydrogen is dissociated into atomic hydrogen by a dissociating material or electromagnetic radiation including UV l ight provided by photon source 205 such that the dissociated hydrogen atoms contact a mol ten, l iquid, or solid solution of the energy holes. The atomic (molecular) hydrogen releases energy as its electrons are stimulated to undergo transiti ons to lower energy levels by the energy holes. Alternative ly, the hydrogen dissociates on the inner surface 240, diffuses though the wal l 250 of the first vessel 200 and contacts a source of energy holes on the outer surface 245 or a solution of energy holes in the molten, l iguid, or sol id state as hydrogen atoms or recombined hydrogen molecules. The atomi c (molecular) hydrogen releases energy as its electrons are stimulated to undergo transitions to lower energy leve ls by the energy holes The electrocatalytic couple is regenerated spontaneously or via a regenerat ion means including heat in means 230 and current source 225 The lower-energy hydrogen is removed from vessel 200 and/or vessel 220 by a means to remove the lower-energy hydrogen sucn as a selective venting valve means 201 whi ch prevents the exothermic shrinkage reaction from coming to equi l ibrium To control reaction rate (the power output), an electric current is passed through the material having a source of energy holes equal to the resonance shrinkage energy with current source 225, and/o the first reaction vessel 200 and the second reaction vessel 220 are heated by heating means 230. The heat output is monitored with thermocouples present in at least the first vessel 200, the second vesse 220, and the heat exchanger 60 of Figure 5. The output power is control led by a computerized monitoring and control system which monitors the thermistors and controls the means to alter the power output. The lower-energy hydrogen is removed by a means 201 to prevent the exothermic shrinkage reaction from coming to equilibrium. Gas Discharge Energv Reactor A gas discharge energy reactor comprises a hydrogen isotope gas fil led glow discharge vacuum chamber 300 of FIGURE 8, a hydrogen source 322 which supplies hydrogen to the chamber 300, through control valve 325 and a current source 330 to cause current to pass between a cathode 305 and an anode 320. The cathode further comprises a source of energy holes of approximately m X 27.21 eV to cause atomic hydrogen "shrinkage" (including the catalytic couples described in my previous U.S. Patent Application entitled "Energy/ Matter Conversion Methods and Structures, " filed on April 28, 1989 which is incorporated by reference) and/or approximately m X 48.6 eV to cause molecular hydrogen " shrinkage" where m is an integer. A preferred cathode 305 for shrinking hydrogen atoms is a palladium cathode whereby a resonant energy hole is provided by the ionizat ion of electrons from pal ladium to the discharge current A second preferred cathode 305 for shrinking hydrogen atoms comprises a source of energy holes via electron transfer to the discharg current including at least one of beryl lium, copper, platinum, zinc, and tel lurium and a hydrogen dissociating means such as a source of electromagnetic radiat ion including UV light provided by photon source 350 or a hydrogen dissociat ing material inc ludi ng the transition el ements and inner transition el ements inc ludi ng iron, platinum, pal ladi um , zirconium, vanadium, nickel, t itanium, Sc, Cr, Mn, Co, Cu, Zn, Y, Nb, o, Tc, Ru, Rh, Ag, Cd, La, Hf, Ta, W, Re, Os, l r, Au, Hg, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Oy, Ho, Er, Tm, Yb, Lu, Th, Pa, and U The reactor further comprises a means to control the energy dissipated in the discharge current when electrons are transferred from an electron donating species to provide an energy hole for hydrogen atoms (molecules) including pressure control ler means 325 and current (voltage) source 330. The gas discharge energy reactor further comprises a means 301 to remove the lower-energy hydrogen such as a selective venting valve to prevent the exothermic shrinkage reaction ' from coming to equi l ibrium. In another embodiment of the gas discharge energy reactor, the source of energy hole is one of a inelastic photon or particle scattering reaction(s). I n a preferred embodiment the photon source 350 suppl ies the energy holes where the energy hole corresponds to stimulated emission by the photon. In the case of a reactor which shrinks hydrogen atoms, the photon source 350 dissociates hydrogen molecules into hydrogen atoms. The photon source producing photons of at least one energy of approximately n X 27.21 eV, n/2 X 27.21 eV, or 40.8 eV causes stimulated emission of energy as the hydrogen atoms undergo the shrinkage reaction. I n another preferred embodiment, a photon source 350 producing photons of at least one energy of approximately n X 48.6 eV, 95.7 eV, or n x 3 1.94 eV causes stimulated emission of energy as the hydrogen molecules undergo the shrinkage reaction. In another embodiment, a magnetic field is appl ied by magnetic field generator 75 of Figure 5 to produce a magnetized plasma of the gaseous ions which is a nonl inear media. Coupl ing of resonator cavities and enhancement of the transfer of energy between them is increased when the media is nonl inear. Thus, the react ion rate (coupl ing of the hydrogen and energy hole resonator cavities) is increased and control led by providing and adjusting the appli ed magnetic field strength. In one embodi ment of the method of operation of the gas di scharge energy reactor, hydrogen from source 322 is introduced inside of the chamber 300 through control valve 325 A current source 330 causes current to pass between a cathode 305 and an anode 320 The hydrogen contacts the cathode which comprises a source of energy holes of approximately m X 27 21 eV to cause atomic hydrogen "shrinkage" and approximately m X 48 6 eV to cause molecular hydrogen " shrinkage" where m is an integer in a pref erred embodiment, electrons are transferred from an electron donating species present on the cathode 305 to the discharge current to provide energy holes for hydrogen atoms (molecules). In the case of a reactor which shrinks hydrogen atoms, the molecular hydrogen is dissociated into atomic hydrogen by a dissociatin material on the cathode 305 or by a source of electromagnetic radiation including UV light provided by photon source 350 such that the dissociated hydrogen atoms contact a molten, liquid, or solid solution of the energy holes. The atomic (molecular) hydrogen releases energy as it electrons are stimulated to undergo transitions to lower energy levels by the energy holes. The energy dissipated in the discharge current when electrons are transferred from an electron donating species is controlle to provide an energy hole equal to the resonance shrinkage energy for hydrogen atoms (molecules) by controlling the gas pressure from source 322 with pressure control ler means 325 and the voltage with the curren (voltage) source 330. The heat output is monitored with thermocouples present in at least the cathode 305, the anode 320, and the heat exchanger 60 of Figure 5. The output power is controlled by a computerized monitoring and control system which monitors the thermistors and controls the means to alter the power output. The lower-energy hydrogen is removed by a means 301 to prevent the exothermic shrinkage reaction from coming to equilibrium. Refrigeration Means A further embodiment of the present invention comprises a refrigeration means which comprises the electrolytic cell of FIGURE 6, the pressurized hydrogen gas cel l of FIGURE 7, and the hydrogen gas discharge cel l of F IGURE 8 of the present invention wherein a source of lower-energy atom ic (molecular) hydrogen is supplied rather than a source of normal hydrogen The lower-energy hydrogen atoms are reacted to a higher energy state with the absorption of heat energy according to the reverse of the catalytic shrinkage reaction such as that given by Eqs (43-45), (47-/39), (50-52), (53-55), ( 56-58), (59-61 ), (62 64), (65-67), (68-70), (7 1 -73), and (74-76) The lower-energy hydroge mol ecules are reacted to a higher energy state w ith the absorption of heat energy accordi ng to the reverse of the catalytic shrinkage reaction such as that given by Eqs (282-284), (285-287), (288-290), (292-294), and (295-297) In this embodiment, means 1 01 , 201 and 301 of FIGURE 6, 7, and 8, respectively, serve to remove the norma l hydrogen such as a selective venting valves to prevent the endothermic reaction from coming to equi librium. EXPERIMENTAL VERF1CATI0N OF THE PRESENT THEORY Light Water Calorimetrv Experiments We report that excess heat was observed during the electrolysis o aqueous potassium carbonate (K + /K + electrocatalytic couple); whereas, no excess heat was observed during the electrolysis of aqueous sodium carbonate. The present experimental results are consistent with the release of heat energy from hydrogen atoms where pairs of potassium ions (K + /K + electrocatalytic couple) induce the electrons of hydrogen atoms to relax to quantized energy levels below that of the "ground state " by providing energy holes each of 27.28 eV which stimulate these transitions. The balanced reaction is given by Eqs. (43-45). No excess heat was observed when K2CO3 was replaced by Na2C03. For sodium or sodium ions no electrocatalytic reaction of approximately 27.21 eV is possible, Eq.(46). Methods A search for excess heat during the electrolysis of aqueous potassium carbonate (K + /K + electrocatalytic couple) was investigated using single cel l si lvered vacuum jacketed dewars To simpl ify the cal ibration of these cel ls, they were constructed to have primari ly conduct ive heat losses Thus, a l inear cal ibrati on curve was obtained Two methods of differential caloπmetry were used to determine the cel l constant which was used to calculate the excess enthalpy First, ' the cel l constant was calculated during the experiment (on-the-fly-cal ibrat ion) by turning an internal resistance heater off and on, and inferring the cel l constant from the difference between the losses with and without the heater Second, the cel l constant was determined with no electrolysis processes occurring by turning an internal resistance heater off and on for a wel l stirred dewar cel l, and inferring the cel l constant from the difference between the losses with and without the heater This metho over-estimates the cell constant because there is no gas flow (which adds to the heat losses) The general form of the energy balance equation for the cell in steady state is: 0 = Pgppi + Q htr + Q xs - P gas - Q, oss (29 where P apP ] is the electrolysis power; C^r is the power input to the heater; Q xs is the excess heat power generated by the hydrogen shrinkag process; P gas is the power removed as a result of evolution of H2 and 02 gases; and Qι, oss is the thermal power loss from the cell. When an aqueous solution is electrolyzed to liberate hydrogen and oxygen gasses, the electrolysis power P app ι ( = E app ιi) can be partitioned into two term Pappl = EapplI = P C e11 + Pgas ( 299 An expression for P gas ( = E gas ι) is readily obtained from the known enthalpy of formation of water from its elements: E^ ^P™ (300 (F is Faraday's constant), which yields E gas = 1.48 V for the reaction H2O → H2 + 2 °2 (301 The net faradaic efficiency of gas evolution is assumed to be unity (which was confirmed experimental ly); thus, Eq. (299) becomes Pcell = ( Eappl " 1 -48V ) I ( 302 The cel l was cal ibrated for heat losses by turning an internal resistance heater off and on while maintaining constant electrolysis and by inferring the cel l conductive constant from the difference between the losses with and without the heater where heat losses were primari ly conductive losses through the top of the dewar. When the heater was off, the losses were given by C(T C - T b ) = P ap pi + 0 + Q xs - P gas (303 where c is the conductive heat loss coeff ic ient; Tp is ambient temperature and Tc is the cel l temperature. When a new steady state is establ ished with the heater on, the losses change to. c ( Tc " - T b ) = P ' appl + O htr + 0 ' xs - P ' g as (304 where a prime superscript indicates a changed val ue v-.'hen the heater was on When the fol lowing assumptions apply Q xs = 0 xs> Pappl = P appl> Pgas = P gas ( 305 the cel l constant or heating coefficient a, the reciprocal of the conduct ive loss coefficient(c), is given by the result Tc ' " c a = n ( 306 In al l heater power calculations, the follow ing equation was used Q tr = Ehtr'htr (307 In the case of interm ittent square wave electrolysis with current only during the high voltage interval of the cycle, P app1 of Eq. (299) is calculated as the product of the peak voltage and the peak current and the duty cycle, Do, which is the pulse length divided by the period. p appl = (E app ιl)Dc = (P ce n + P gas )Dc (308 In the case of intermittent square wave electrolysis with current only during the high voltage interval of the cycle and where the net .faπadalc eff iciency of gas evolution is assumed to be unity, P ce η of Eq. (302) becomes p cell = (CE appl - 1.48V)l)Dc (309) Experiments * 1 , *2, and *3 The present experiments were carried out by observing and comparing the temperature difference, ΔT ' ι =T(electrolysis only) - T(blank) and ΔT2 - T(resistor heating only) -T(blank) referred to uni t input power, between two identical 350 ml si lver-coated vacuum- jacketed dewars. One of the calorimeter dewars having the same conf iguration and containing the same amount of el ectrolyte, same electrodes (nickel cathode and Pt anode ), resistor-heater, thermistor, stirred at the same speed, was used as the blank. In this dewar neither electrolysis nor heating by the resistor was carr ied out. Experiments were also carried out by using the blank dewar from a previous experiment as the working dewar and vice versa. This exchange was done to ensure that the effect is not due to any difference in the thermal properties of the two specif ic dewars used Each cel l was assembled comprising a 350 ml silvered vacuum jacketed dewar (Cole Palmer Model # 8600) w ith a 7 cm opening covered with a 0 75 inch thi ck Styrofoam stopper l ined with Paraf i lm The experimental apparatus for the differential calorimetry used for these studies is shown in FIGURE 9 The heating coeff icients were calculated from ΔT i a = — (31 0 Pcell ΔT2 a = n ( 31 1 Q htr The outside of the cel ls were maintained at ambient air temperature which was monitored. Ambient temperature fluctuations per 24 hours were typical ly less than 0.5 °C. The cathode comprised 24 meters of 0.127 mm diameter nickel wire (99 % Alfa * 10249, cold drawn, clean Ni wire) that was coi led about the central Pt anode. The cathode was cleaned by placing it in a beaker of 0.57 M K2CO3 /3% H2O2 for 30 minutes and then rinsing it with distilled water. The leads were inserted into Teflon tubes to insure that no recombination of the evolving gases occurred. The anode was a 10 cm by 1 mm diameter spiraled platinum wire (Johnson Matthey) with a 0.127 mm Pt lead wire. The leads were inserted into Tef lon tubes to prevent recombination, if any, of the evolving gases. The cathode-anode separation distance was 1 cm. As usual in electrochemistry, measures were taken to avoid impurities in the system, especially organic substances. We note here the known problems with the reproducibility of the hydrogen overpotential which can be overcome only by ensuring the lowest possible level of impurities The following procedures were appl ied in order to reproduce the excess heat effect Before starting the experiment, the electrolysis dewar was cleaned w ith Alconox and 0. 1 M nitric acid and rinsed thoroughly with disti l led water to remove al l organic contaminants. The Pt anode was mechanical ly scoured with steel wool, ' soaked overnight in concentrated HNO3, and rinsed wi th disti l led water The ni ckel cathode was removed from its conta iner wi rubber gloves, and cut and folded in such a way that no organic substances were transferred to the nickel surface. The nickel cathode was di pped into the worki ng solut ion under e lectrolysis current and never left in the working solution -w ithout electrolysis current. In Experiments * 1 and *2, the electrolyte solution was 200 ml of 0.57 M aqueous K2CO3 (Aldrich K2CO3 * - H2O 99 + %); in Experiment *3, the electrolyte solution was 200 m l of 0.57 M aqueous Na2C03 (Aldrich Na2C03 A.C.S. primary standard 99.95 + %). The resistance heater used during cal ibration and operation was a 10 ohm 1 % precision metal oxide resistor in a 2 mm outer diameter • Tef lon tube The heater was powered by a variable DC vol tage power source d 0.5%). The heating power was calculated using Eq. (307). The electrolyte solution was stirred with by a 7 mm by 2 cm prolate spheroid magnetic stirring bar which was spun by a 6 cm long open magnet mounted on an open shaft revolving at 750 RPM under the dewar. The shaft was that of an open mixing motor (Flexa-Mix Model 76, Fisher). Elimination of erroneous attribution of the effect to temperature gradients was carried out by testing for minute spatial variations of th temperature over time. Three thermistors were positioned at about 2.5 cm apart from each other at the bottom, middle, and upper part of the electrolyte. No difference was observed (within the l im it of detection, 0.01 °C) . Voltage (1 0.5%), Current (1 1 %), and temperature d 0. 1 β C) data were acquired by a data acquisition system comprising an Apple Mac I I S 5/80 with a NU bus adapter and the following G W Instruments, Inc. hardware: GWI - 625 Data Acquisition Board, GWI - J2E Multiplexer, GWI - ABO Analog Breakout System, GWI - 34W Ribbon cable. P app ι was given by Eq (299) as the product of the vol tage and the constant current, and P ce iι was given by Eq. (302). The current voltage parameters for Experiment ~2 were an periodi square-wave having an offset voltage of 1.60 volts, a peak voltage of 1 .90 volts, a peak constant current of 47.3 mA, a 36.0% duty cycle, and a frequency of 600 Hz Peak voltage measurements were made with an os i l loscope (BK model -21 20), and the time average current was 31 determined from a mult imeter voltage measurement (+_ 0 5%) across a cal ibrated resistor ( 1 ohm) in series with the lead to the cathode The waveform of the pulsed cel l was a sguare wave Since there was curre only during the p al- voltage interval of the cycle, P apπ ι was given by Eg (308) and P ce ι, was given by Eq (309). The faradaic effic iency of gas production by the working potassiu cel ls was studied Comparing this result with the sodium systems allows the accuracy of the analysis to be seen. A closed cell was fashioned from a 150 ml round bottom flask, 2 cm X 2 mm prolate spheroid stir bar, a glass "Y" adapter, glass tubing bent into the shape o one cycle of a square wave, a 150 ml beaker and a 0.01 ml graduated buret. The cell was set up to mimic as closely as possible the calorimetry tests. A constant current (+. 0.1 %) supply was used to suppl the power for the electrolysis. Current measurement was done with a Heathly multimeter (_ 0.1 %). Gas was col lected and measured in the buret. Several experiments were run to ensure the cell was sealed tightly. Light Water Calorimetry Results Mills' theory [Mills, R., Unification of Spacetime. the Forces- Matter, and Energv. Technomics Publishing Company, Lancaster, PA, ( 1992)] predicts that the exothermic catalytic reaction whereby the electrons of hydrogen atoms are stimulated to relax to lower energy levels corresponding to fractional quantum states by providing energy holes which stimulate these transitions will occur during the electrolysis of K2CO3 light-water solutions but will not occur during the electrolysis of Na2C03 light-water solutions. The results of the electrolysis with a nickel wire cathode at 83 mA constant current and heater run of K2CO3 appear in FIGURE 1 0 and TABLE 1 The heating coefficient of the heater run (calibration) was 41 °C/W.; whereas, the heating coefficient of the electrolysis run was 87 °C/W The production of excess enthalpy was observed The higher the heating coefficient, th more heat released in the process The results of the electrolysis of a K2CO3 electrolyte with a nickel cathode and a periodic square-wave having an offset voltage of 1.60 volts, a peak voltage of 1 90 volts; a peak constant current of 47.3 mA, a 36 0% duty cycle, and a frequency of 600 Hz appears in FIGURE 1 1 and TABLE 1 The output power was 16 times the ohmic i nput power The results of the electro lysis at 81 mA constant current and the heater run of Na2C0 appear in FI GURE 1 2 and TABLE 1 The heating coefficient of the electrolysis run was 47 °C/W; whereas, the heating coeff icient of the heater run (cal ibration) was 46 "C/W The production of excess heat was not observed. The data of the faradaic efficiency of the production of gas by a working potassium cell and a control sodium cel l appear in TABLE 2. Fo both K2CO3 and Na2 03, the production of electrolysis gases was 100% faradaic efficient. Discussion Almost all electrolysis experiments will be similar to the case of Na2C03, above which does not provide an energy hole of approximately 27.21 eV (Eq. (46)). Only a few combinations of electrolytes/electrodes such as the K2CO3 case above which provide an energy hole of approximately 27.21 eV (Eqs. (43-45)), will yield excess heat. NEW HYDROGEN ATOM Extreme Ultraviolet Spectrum of Hvdrino Atoms Hydrogen Transitions to Electronic Energy Levels Below the "Groun State " Corresponding to Fractional Quantum Numbers (Eq. (6)) Exactly Match the Spectral Lines of the Extreme Ultraviolet Background of Interstellar Space. Hydrogen transitions to electronic energy levels below the n = 1 state have been found in the spectral lines of the extreme ultraviolet background of interstel lar space This assignment resolves the paradox of the identity of dark matter. It also accounts for other celestial observations such as: diffuse Hα emission is ubi quitous throughout the Galaxy, and widespread sources of f lux shortward of 91 2 A are reguired to account for thi s emission [Mi l ls, R., Good, W., Unif ication of Spacetime. the Forces, Matter, and Energv, Technomics Publ ishing Company, Lancaster, PA, ( 1992), pp 169- 172; Farrell, J., Good, W., Mi lls, R , J of Astrophysics, ( 1993) in progress] The Un iverse is predominantly comprised of hydrogen and a proport ional ly smal l amount of helium These elements are expected to exi st i n i nterstel l ar regions of space at low temperature and comprise the majority of interste l la' matter However, to be consi stent wi th gravitational observat ions, the universe is comprised of nonluminous weakly interact ing matter, dark matter, which may account for the majority of the universal mass Dark matter exists at the cold fringes of galaxies and in cold interstel lar space. The gravitational influence of its mass accounts for the observed constant angular velocity of many galaxies as the distance from the luminous galactic center increases. The identity of dark matter is a cosmological mystery. Postulated assignments include τ neutrinos [Davidsen, A., et al., "Test of the decaying dark matter hypothesis using the Hopkins ultraviolet telescope", Nature, 351 , ( 1991 ), pp. 128- 130]; but a detailed search for signature emissions has yielded ni l [Davidsen, A., et al., "Test of the decaying dark matter hypothesis using the Hopkins ultraviolet telescope " , Nature, 351 , ( 1991 ), pp. 128- 130]. It is anticipated that the emission spectrum of the extreme ultraviolet background of interstellar matter possesses the spectral signature of dark matter. Labov and Bowyer have observed an intense 635 A emission associated with dark matter [Labov, S., Bowyer, S., "Spectral observations of the extreme ultraviolet background " , The Astrophysical Journal, 371 , ( 1991 ), pp. 810- 819]. " Regardless of the origin, the 635 Λ emission observed could be a major source of ionization. Reynolds ( 1983, 1984, 1985) has shown that diffuse Hα emission is ubiquitous throughout the Galaxy, •and widespread sources of flux shortward of 91 2 A are required. Pulsar dispersion measures (Reynolds 1989) indicate a high scale height for the associated ionized material. Since the path length for radiation shortward of 912 A is low, this impl ies that the ionizing source must a lso have a large sca le he ight and be widespread Transient heat ing appears unlikely, and the steady state ionization rate is more than can be provided by cosmic rays, the soft X-ray background, B stars, or hot whi te dwarfs (Reynolds 1 86, Brushwei ler & Cheng 1988) Sciama ( 1 990) and Salucci & Sciama ( 1990) have argued that a variety of observati ons can be explained by the presence of dark matter in the galaxy which decays with the emission of radiation below 912 A The flux of 635 A radiation required to produce hydrogen ionization is given by F = ζ H /σ λ = 43 x 10 4 ζ_ 13 photons cm -2 s- ' where ζ_ 13 is the ionizing rate in units of 10 ~13 s _1 per H atom Reynolds (1986) estimates that in the immediate vicinity of the Sun, a steady state ionizing rate of ζ_ 13 between 0.4 and 3.0 is required To produce this range of ionization, the 635 A intensity we observe would have to be distributed over 7% - 54% of the sky. " Labov and Bowyer further report [Labov, S., Bowyer, S., "Spectral observations of the extreme ultraviolet background " , The Astrophysical Journal, 371, (1991), pp.810-819] in their raw data the high resolution raw spectral data of the extreme ultraviolet background emitted from dark interstellar space covering the range 80 A - 650 A. Peaks are present at 85 A, 101 A, 117 A, 130 A, 140 A, 163 A 182 A, 200 A, 234 A, 261 A, 303 A, 460 A, 584 A, 608 A, and 633 A. In TABLE 3, we assign these peaks to the hydrogen electronic transitions to energy levels below the "ground state" corresponding to fractional quantum numbers. Conspicuously absent is the 256 A (48.3 eV) line of He II which eliminates the assignment of the 303 A and the 234 A lines to the He I! transitions. The 304 A (40.8 eV) transition of hydrogen is scattered by interstellar neutral helium giving rise to a broad He I emission centered at 584 A (21.21 eV) and a broad scattered hydrogen emission at about 634 A (19.6 eV). Similarly, the 114 A (108.8 eV) transition of hydrogen is scattered by interstellar neutral helium giving rise to a broad He I emission centered at 584 A (21.21 eV) and a broad scattered hydrogen emission at about 141 A (87.6 eV) Also, the 182.3 A (68 eV) transition of hydrogen is scattered by interstellar neutral helium giving rise to a broad He I emission centered at 584 A (21.21 eV) and a broad scattered hydrogen emission at about 265 A (46.8 eV) Another two-decade-old cosmological mystery is the discrepancy between solar neutrino flux observed with the Homestake detector , 21 + . 005 SNU , and that predicted based on the Standard Solar Model , 7.9 26 SNU According to the Standard Solar Model, the pp chain is the predominant energy source of main-sequence stars which commences 1 37 with proton proton fusion according to the fol low i ng react ion [Bahcal l , J , et al., " So lar neutrinos a f ield in transition " , Nature, 334, 1 1 , ( 1 98 pp 487-493], i H + Η - 2 H + e + + υ ( 3 1 And, according to this model , strong coupl ing exists between luminosit and neutrino f lux because they are both based on nuclear react i ons In resolution of this problem, we propose that a major portion of the ene emi tted by the sun derives from hydrogen electronic transitions to energy levels below the "ground state " which can yield energies per at comparable to nuclear energies. Data strongly supporting this tenant i the observation by Labov and Bowyer of an intense 304 A (40.8 eV) sola emission line corresponding to the l -* l /2 transiti on of hydrogen in the absence of the 256 A (48.3 eV) line of He I I which eliminates the assignment of the 304 A l ine to the He I I transition. Identification of Hydrino Atoms bv ESCA We report the product atom of an exothermic reaction wherein energy holes, each of approximately 27.21 eV, are provided by electrochemical reactants (K + /K + electrocatalytic couple) which caus heat to be released from hydrogen atoms as their electrons are stimulated to relax to quantized potential energy levels below that of the " ground state". The energy removed by an energy hole, is resonant with the hydrogen energy released to stimulate this transition. Excess heat was observed during the electrolysis of aqueous potassium carbonate (K + /K + electrocatalytic couple); whereas, no excess heat wa observed during the electrolysis of agueous sodium carbonate. Samples of the cathodes of the potassium carbonate cel l and the sodium carbonate electrolytic cell were analyzed by ESCA (Electron Spectroscopy for Chem ical Analysis). A broad 544 eV peak was presen only in the case of the potassium carbonate cel l The binding energy of H*( 1 /2), the predicted lower-energy hydrogen atom having its electron in the 1 /2 quantum state, is 54 4 eV The data was consistent with the ass ignment of the broad 54 4 eV peak to H*( 1 /2) as the product of an exothermic reaction wherein the electrons of hydrogen atoms are stimulated to relax to quant ized potential energy leve ls below that of the " ground state via elt-cti υchemical reactants κ + and l< + which provide energy holes which stimulate these transitions Methods The hydnno atom was identified by ESCA (Electron Spectroscopy for Chemical Analysis) We report H (i/2) production as identified by ESCA of the cathode of an electrolysis cell comprising a nickel cathode and a light water K2CO3 electrolyte ESCA (.Electron S_pectroscopy for Chemical Analysis) is capable of 0.1 eV resolution of E , the binding energy of each electron, of an atom. In general, ESCA requires a photon source with energy E v These photon ionize electrons from the sample being analyzed. These ionized electrons are emitted with energy E inetic : Ekinetic = Ehv " Eb - E Γ (313 where Eb is the binding energy of the electron, and E r is a negligible recoil energy. The kinetic energies of the emitted electrons are measured by measuring the magnetic field strengths necessary to have them hit a detector. Since Ekinetic and Ehv are experimentally known, Eb can be calculated. The binding energies of all atoms and materials of an experiment are known or can be measured using controls; thus, an.ESCA analysis can provide an incontrovertible identification of an atom. The binding energy of the various hydnno states are known, and an expected ESCA hydrino spectrum can be predicted. The binding energies are 1 1 1 1 Eb =^z 13 . 6 eV n = 2 ' 3 ' 4 "" (314 The binding energies of the various hydrino quantum states are given in TABLE 4. Experimental A search for the hydnno atom, lower-energy atomic form of hydrogen, in the nickel cathode immediately following the electrolysis of aqueous potassium carbonate (K + /K + electrocatalytic couple) was conducted using ESCA where the cathode of a sodium carbonate electrolytic cell was the control In each case, the cathode was a 75 cm wide by 5 cm long by 0125 mm thick nickel foil (Aldrich 999+%, cold rolled, clean Ni) spiral of 9 mm diameter and 2 mm pitch with z nickel lead strip The nickel 873 1 39 cathode v. as prepared by tight ly rol l ing the nickel f oi l about a 9 mm ro The rod was removed The spiral was formed by part ial ly uncoi l ing the foi l The cathode was soaked in 3% H 2 O /0 57 M X 2 C0 5 (X = K where the electrolyte of the ce l l was K2CO3, X = Na v Uere the electrolyte of the cel l was Na2 03 solut ion for 30 minutes The cathooe was thoroughly rinsed w ith disti l led water The leads were inserted into Teflon tubes to insure that no recombination of the evolving gases occurred In each case, the anode was a 10 cm by 1 mm diameter spiraled platinum wire (Johnson Matthey) with a 0.127 mm Pt lead wire. The leads were inserted into Teflon tubes to prevent recombination, if any, of the evolving gases. The cathode-anode separation distance was 1 cm. As usual in electrochemistry, measures were taken to avoid impurities in the system, especially organic substances. We note here the known problems with the reproducibility of the hydrogen overpotential which can be overcome only by ensuring the lowest possible level of impurities. The following procedures were applied in order to reproduce the excess heat effect. Before starting the experiment, the electrolysis dewar was cleaned first with Alconox and rinsed with distilled water and then 0. 1 M nitric acid and rinsed thoroughly with distilled water to remove all organic contaminants. T Pt anode was mechanically scoured with steel wool, soaked overnight i concentrated HNO3, and rinsed with distilled water. The nickel cathode was removed from its container with rubber gloves, and cut and folded such a way that no organic substances were transferred to the nickel surface The nickel cathode was dipped into the working solution under electrolysis current and never left in the working solution without el ectrolysis current The electrolyte solution of the potassium cel l was 200 ml of 0.57 3 M aqueous K2CO3 (Alpha K2CO3 * - H 2° 99+%) The electrolyte solution of the sodium cel l was 200 ml of 0.57 M aqueous N32CO3 (Aldrich Primary Standard Na2C0 99 9+%) A constant current of approximately 80 mAmps was appl ied for 3 hours at which t ime each cathode was removed In each case, a cathode sample on the outer surface closest to the anode was cut off, rinsed ith disti l led water, and examined by ESCA 40 [The methods, experimental , and results of the l i ght water calorimetry during the electrolysis of potassium carbonate and sodium carbonate electro lyt i c solut ions are gi ven in the L ight Water Calorimetry Sect ion Results of the I dent i f icat ion of the Hydn no Atom by ESCA The results of the ESCA analysis of a control nickel sheet appears in FIGURE 1 3. The results of the ESCA analysis of a sample of the nickel cathode from each of an aqueous potassium carbonate electrolytic cell and a control aqueous sodium carbonate electrolytic cell are shown juxtapose in FIGURES I 4A- 14D. Discussion The ESCA analysis of FIGURE 14A shows a broad peak at the bindin energy of 54.4 eV for the cathode from the potassium carbonate cell and the absence of this peak for the cathode from the sodium carbonate cell. There is no known atom which has an electron with a binding energy in this region that was present in the electrolytic cell. As shown in TABLE 4, the binding energy of H*( 1 /2), the hydrino atom having its electron in the 1 /2 quantum state, is 54.4 eV. The data is consistent with the assignment of the broad 54.4 eV peak to H*( l /2) as the product of an exothermic reaction wherein the electrons of hydrogen atoms are stimulated to relax to quantized potential energy levels below that of the " ground state" via electrochemical reactants K + and K + which provide energy holes which stimulate these transitions according to Eqs. (43-45). NEW HYDROGEN MOLECULE Mass Spectroscopic I dent ification of the Dihydrino Molecule We report the product molecule of an exothermic reaction wherei n energy holes, each of approximately 27 21 eV, are provided by electrochem i cal reactant s (K + /K + electrocatalytic couple) which cause heat to be released from hydrogen atoms as their electrons are stimulated to relax to quant ized potent ia l energy leve ls below that of the " ground state " The energy removed by an energy hole, is resonant with the hydrogen energy released to stimulate this transition Electrolysis gases were collected from pulsed and continuous current electrolysis of aqueous potassium carbonate (KVK + electrocatalyt ic couple) w ith a nickel cathode as wel l as those of an identical control sodium carbonate electrolytic cel l For the pulsed potassium electrolytic cel l, the previously reported [Mi l ls, R., Good, W., Shaubach, R., " Dihydrino Molecule Identification " , Fusion Technology, in progress. ] excess power of 41 watts exceeded the total input power given by the product of the electrolysis voltage and current by a factor greater than 8. No excess power was produced by the sodium carbonate electrolytic cel l. The product of the exothermic reaction is hydrogen atoms having electrons of energy below the "ground state" which are predicted to for molecules. The predicted molecules were purified from electrolytic gases by cryofiltration. Mass spectroscopic analysis showed a species with a mass to charge ratio of 2 having a higher ionization potential tha that of the hydrogen molecule. Method A hydrino atom, hydrogen atom with its electron in a lower than "ground state" energy level corresponding to a fractional quantum number, has an unpaired electron and would bind to the nickel cathode. Bound hydrogen atoms demonstrate a high degree of mobility as shown b EELS (Electron Energy Loss Spectroscopy) [Nieminen, R., Nature, Vol. 365 March, ( 1992), pp. 289-290]. Hydrino atoms are predicted to possess hig mobi lity which permits the possibility of subseguent shrinkage reactions as well as dihydrino molecule forming reactions. Dihydrino molecule forming reactions can occur between hydπnos in comparable quantum states as well as between hydrinos and protons and electrons and between hydrinos and hydrogen atoms. A preferred method to identify the dihydrino molecule is via cryof i ltration fol lowed by the search for mass spectroscopic anomal ies Experimental 42 The dihydr ino molecule was identi fied by mass spectroscopy We report H*2' 2C production as identif ied by mass spectroscopy o XX the cryof i l tered gasses evolved f rom an el ectrolys is cel l c ompr ising a nickel cathode and a l ight w ater K2CO3 electrolyte The dihydrino molecule was predicted to be spin paired, to be smal ler than the hydrogen molecule, to have a higher ionization energy than H2, and to have a lower l iquefaction temperature than H2 Dihydrin molecules present in the gases evolved from an electrolytic cel l having an electrolyte of the electrocatalytic couple, K + /K + , were separated from normal hydrogen by cryofiltration. Following cryofiltration, the dihydrino molecule was distinguished from normal molecular hydrogen using mass spectroscopy. Mass spectroscopy distinguished a sample containing dihydrino molecules verses a sample containing H2 by the showing a different ion production efficiency as a function of ionization potential and a different ion production efficiency at a given ionization potential for the two samples. Data from Experiment 14 [Mil ls, R., Good, W., Shaubach, R., "Dihydrino Molecule Identification", Fusion Technology, in progress] wer recorded over a 240 day period at an operating condition of 1 Hz, 10 amperes, and 20% duty cycle. Data for day 120 are recorded in TABLE 1 of [Mil ls, R., Good, W., Shaubach, R., "Dihydrino Molecule I dentification", Fusion Technology, in progress] and show 41 watts of output with an output to input ratio of about 22 assuming 100% Faradaic efficiency. An identical electrolytic cell with a sodium carbonate electrolyte showe no excess heat. We col lected 1000 ml of the electrolysis gases from Experiment * 1 4 [Mil ls, R., Good, W , Shaubach, R., "Dihydrino Molecule I dentification", Fusion Technology, in progress] which produced 39. 1 watts of excess power according to the exothermic reaction given by Eqs (43-45) in a high vacuum gas collection bulb as wel l as electrolysis gases from an identical electrolytic cel l with a sodium carbonate electrolyte that showed no excess heat The electrolys is gases and a standard hydrogen sample were cryof i ltered and col lected in two port 250 ml high vacuum sample bulbs A schematic of the cryof i l trati on apparatus appears in F I GURE 1 5 A sample bulb -was also f i l l ed w i th st andard hydrogen, and gases were col lected from the cryof i l ter alone Mass spectroscopy of cryof i ltered electrolysis gas sampl es from a sodium carbonate and the potassium carbonate el ectrolyt ic cel l as wel l as standard hydrogen, cryof i ltered standard hydrogen, and gases from th cryof i lter alone were performed whereby the intensity of the m/e = 1 and m/e = 2 peaks was recorded wh i le varying the ionizat ion potential (I P) of the mass spectrometer. The entire range of masses through m/e 50 was measured fol lowing the determinations at m/e = 1 and m/e = 2. In all cryofiltered samples, the only peaks detected in this mass range were those consistent with trace air contamination (argon, nitrogen, oxygen, water vapor) and trace CO2. The mass spectroscopy was performed by Schrader Analytical and Consulting Laboratories, Inc. using a AEI MS 30 with a VG 7070 source set at a sensitivity of 700. The ionization energy was cal ibrated to within i 1 eV. The volume of sample gas injected into the mass spectrometer at each ionization potential setting was made identical by evacuating the connection between the sample and a stopcock of the spectrometer then opening the evacuated volume to the sample vessel. Results of the Mass Spectroscopic I dentification of the Dihydrino Molecule The results of the mass spectroscopic analysis with varying ionization potential of standard hydrogen are given in TABLE 5. In independent experiments, it was determined that the results of the mass spectroscopic analysis with varying ionization potential of standard hydrogen was independent of mass spectrometer sensitivity and sample pressure The results of the mass spectroscopic analysi s w ith varying ion izat ion potential of cryofi ltered standard hydrogen are given in TABLE 6 The results of the mass spectroscopic analysis w ith varying ionizat ion potent ial of gases from the cryofi lter alone are given in TABLE 7 AA The results of the r xz, spectroscopic analysis with varying ionization potential of cι oτ 1 ltered electrolysis gases evolved from the sodium electrolytic cell a r e given in TABLE 8 The results of mai- Ξrectroscopic analysis with varying ionizatio potential of cryofiltereu eiectrolvsis gases evolved from the potassium electrolytic cell are given in TABLE 9 and FIGURE 16 Discussion The dihydrino molecule, H*2J 2c " = has a higher ionization energy than H2 This was observed by measuring the intensity of the m/ = 1 and m/e = 2 peaks while varying the ionization potential (IP) of the mass spectrometer. The ionization reaction of H2 is H 2 (g) → H 2 (g) + + e ~ IE = 15.46 eV (315 The ionization energies of water are 12.61, 14.8, 18.8, and 32 eV. The data of TABLE 9 and FIGURE 16 demonstrate that no m/e = 2 is present a an ionization potential above the threshold for the ionization of molecular hydrogen as shown in TABLE 5, but a m/e = 2 peak is present at a significantly higher ionization potential, 63 eV. The cryofilter removes essentially all of the standard hydrogen as shown by the data o TABLE 6. The cryofilter does not release any unusual species with a mass to charge ratio of 2 as shown by the data of TABLE 7. The cryofiltered electrolytic gases from the sodium carbonate cell does not contain any unusual species with a mass to charge ratio of 2 as shown b the data of TABLE 8. The data are consistent with the assignment of the m/e = 2 of the cryofiltered electrolytic gases from the potassium carbonate cell to H*2! 2C = r the dihydrino molecule, as the product of an exothermic V2 reaction wherein the electrons of hydrogen atoms are stimulated to relax to quantized potential energy levels below that of the " ground state " via electrochemical reactants YX and K + which provide energy holes which stimulate these transitions The observed experimentally measured ionization energv of 63 + . 1 eV is consistent with the theoretical ionization energy of 6227 eV given by Eg (258) TABLE 1. ^ \ 1 U / 2 T-2 TABLE 2. Faraday ' s Calculated Measured Efficienc Electrolyte gas (mmol) Volume (mL) Volume (mL ) (%) 0.57M K2CO3 1.961 49.91 51.30 102.8 0.57M Na 2 C0 3 1.955 49.69 49.86 100.3 TABLE 3 a For hydrogen transitions, the energy Is given by Eq. (6); aFor helium Compton scattered peaks of hydrogen transitions, * Bowyer and Lab 230A, 230-430A, discrepancy betw T-4 T-5 TABLE 5. 0 2.5 5.4 6.8 T-6 TABLE 6. 0 0.005 0.005 T-7 TABLE 7. Ionization Potential Intensity of Signal ( volts) <s Mass to Charge Ratio ( cv ) ( m/e) 0 0 0 T-δ TABLE 8. 0.004 0 0.025 T-9 TABLE 9. 22.7 0.010 0.025 45.1 0.024 0.020 78.9 0.060 0.240

Claims: 1 5 CL AI MS 1 A hydrogen atom having the property that us el ectron is in a lower than " ground state " energy level which corresponds to a f ract ional quantum number 2 A method of isolating the hydrogen atom of c laim 1 , compromisi ng the steps of isolati ng the hydrogen atom v ia cryof i l trat ion, and identifying the hydrogen atom by searchi ng for mass spectroscopi c anomal ies. 3. A method of releasing energy, comprising the steps of: sel ecting an element of matter having a nucl eus and at least one electron disposed in a first electron orbital; determining the resonance shrinkage energy of the electron orbital and an energy hole that wil l stimulate the at least one electron to undergo a resonance shrinkage transition to relax to a guantized potential energy level below that of a " ground state" of said element of matter, thus defining a second electron orbital- of smaller dimensions than said f irst electron orbital; providing said energy hole substantially equal to the resonance shrinkage energy of the element of matter; juxtaposing said element of matter and said energy hole; whereby the at least one electron of the element of matter is stimulated by said energy hole to undergo at least one shrinkage, thus ■ releasing energy. 4. The method of claim 3, wherein the step of providing the energy hole comprises providing a catalytic system where at least one electron is transferred from one of a first atom, ion, and mol ecule to one of a second atom, ion, and molecul e. 5 The method of claim 4, wherein a sum of two ionization energies of said f irst atom, ion, or molecule less a sum of two ionizat i on energi es of sai d second atom, i on, or mo lecule is approx imately 27 2 1 eV 6 The method of c laim 3, wherein the step of providing the energv hole comprises a catalytic system, wherein the overal l reacti on is 1 6 a H H , ( p + 1 ) ( P -P 2 ] x 1 3 6 where a 0 is the orbitsphere radius and p represents the number of cyc les 7 A pressurized gas energy reactor, comprisi ng means for containing a source of hydrogen; means to dissociate the hydrogen into atom ic hydrogen, means for bringing the dissociated hydrogen atoms into contact with one of a molten, liquid, or sol id solution of energy holes, and means for removing lower-energy hydrogen so as to prevent an exothermic shrinkage reaction from coming to equilibrium. 8. A hydrogen molecule having the property that its electron ' s are in a lower than "ground state" energy level which corresponds to a fractional quantum number. 9. A method of isolating the hydrogen molecule of claim 8, compromising the steps of: isolating the hydrogen atom via cryofiltration; and identifying the hydrogen molecule by searching for mass spectroscopic anomal ies. 10. A method of releasing energy, comprising the steps of: selecting an element of matter having at least two nuclei and two electrons disposed in a first electron orbital; determining the resonance shrinkage energy of the electron orbital and an energy hole that wil l stimulate the at least two electrons to undergo a resonance shrinkage transition to relax to a quantized potential energy level below that of a "ground state " of said element of matter, thus defining a second electron orbital of smal ler dimensions than said first electron orbital, providing said energy hole substantial ly equal to the resonance shrinkage energy of the element of matter; juxtaposing said el ement of matter and said energy hole, whereby the at least two electrons of the element of matter are st i mulated by sai d energy hole to undergo at least one shrinkage, thus re leasing energy 1 1 . The method of claim 10, wherein the step of provid ing the energy hole comprises providing a catalytic system where at least one 47 electron is transferred from one of a first atom, ion, and molecule to one of a second atom, ion, and molecule 12 The method of claim 11, wherein the ionization energy of said first atom, ion, or molecule less a the ionization energy of said second atom, ion, or molecule is approximately m x 486 eV 13 The method of claim 10, wherein the step of providing the energy hole comprises a catalytic system, wherein the overall reaction is: where 2c ' is the internuclear distance of the hydrogen-type molecule; the energy hole is mp 2 X 48.6 eV where m and p are integers; during the transition, the elliptic field is increased from magnitude p to magnitude p + m; the total energy, ET, released during the transition is Eτ = -13.6eV " ( 2 (m + P )2V2 - (m + P + 13.6eV 2 P 2 2 - P 2 2 + 14. An electrolytic cell energy reactor, pressurized gas energy reactor, and a gas discharge energy reactor, comprising: means for containing a source of hydrogen; means for bringing the hydrogen molecules into contact with one of a solid, molten, liquid, or gaseous solution of energy holes; and means for removing the lower-energy hydrogen so as to prevent an exothermic shrinkage reaction from coming to equilibrium. 148 15. A method of releasing energy, comprising the steps of: selecting an element of matter having a nucleus and at least one electron disposed in a first electron orbital; determining the resonance shrinkage energy of the electron orbital and the energy hole which will stimulate the electron to undergo a resonance shrinkage transition to relax to a quantized potential energy level below that of a ground state of said element of matter, defining second electron orbital of smaller dimensions that said first electron orbital forming a shrunken orbital of the element of matter; providing said energy hole substantially equal to the resonance shrinkage energy of the element of matter; juxtaposing said element of matter and said energy hole; whereby the electron of the element of matter is stimulated by said energy hole to undergo at least one shrinkage and energy is released thereby. 16. The method of claim 15, wherein the step of providing an energy hole comprises providing a catalytic system including an electrochemical reactant comprising at least one of a cation and an anion. 17. The method of claim 15, wherein said step of providing an energy hole comprises selecting a second element of matter having an ionization energy substantially equal to the resonance shrinkage energy of said first element of matter. 149 18. Apparatus for providing the release of energy, comprising: means for providing an element of matter in a selected volume, said element having a nucleus and at least on electron disposed in a first electron orbital having a resonance shrinkage energy; and means introduced into said selected volume for providing an energy hole in juxtaposition with said element of matter, said energy hole having a magnitude substantially equal to said resonance shrinkage energy, wherein: the electron of the element of matter is catalyzed by the energy hole to undergo at least one shrinkage transition thereby to release energy. 19. The apparatus of claim 18, wherein said means providing an energy hole is a substance comprising at least a second element of matter having an ionization energy substantially equal to the resonance shrinkage energy of said first element of matter. 20. The apparatus of claim 18, wherein said means providing an energy hole comprises a catalytic system including an electrochemical reactant comprising at least one of a cation and an anion. 150 21. The apparatus of claim 19, wherein said first element of matter comprises one of 1H; 2H and 3H; and said second element comprises K + and K+. 22. The apparatus of claim 19, further including an electrolytic cell comprising at least a cathode; an anode; an electrolytic solution; a vessel; a power supply providing a current; a means to control said current; an external energy source; and a means to control the pressure of the vessel. 23. The apparatus of claim 22, wherein the cathode is nickel or graphite. 24. The apparatus of claim 22, wherein the anode is platinum or nickel. 25. The apparatus of claim 22, wherein the electrolytic solution is aqueous potassium carbonate. 26. The apparatus of claim 25, wherein the aqueous electrolytic solution is basic. 27. The apparatus of claim 22, wherein the current control means provides intermittent current of an intermittent square- wave having an offset voltage of approximately 2.5 volts to 2.2 volts; a peak voltage of approximately 3 volts to 2.75 volts; a 151 peak current of approximately 175 mA; approximately a 40% duty cycle; and a frequency of approximately 300Hz - 1500Hz. 28. The apparatus of claim 22, wherein the electrolysis cell is operated at a temperature above room temperature. 29. The apparatus of claim 19, wherein the source of an energy hole is a single cation, neutral atom, or anion or a single molecule which is a cation, neutral molecule or anion, or is a combination of said species wherein the said energy hole is substantially equivalent to n/2 27.21 eV where n is an integer. 30. The apparatus of claim 18, wherein said means providing an energy hole comprises at least an additional element of matter having an ionization energy, which in combination with the ionization energy of said second element produces said energy hole substantially equal to the resonance shrinkage energy of said first element of matter. 31. The apparatus of claim 19, wherein said first element of matter comprises an isotope of hydrogen and said second element comprises: a single-ion capable of producing energy holes for shrinking hydrogen atoms selected from the group consisting of: Catalytic Ion n nth ionization energy 152 Al 2 AH + Tι2 + As + Rb 1 + Mo 2+ Ru2 + ln + Te2 + where the number following the atomic symbol (n) is the nth ionization energy of the atom, for example, Ti + 27.49eV = Ti 3+ t e " . 32. The apparatus of claim 30, wherein said first element of matter comprises an isotope of hydrogen and said second and said additional elements of matter comprise one of: (1) a two-ion couple capable of producing energy holes for shrinking hydrogen atoms, selected from the group consisting of: 153 cr r 154 55 56 157 158 159 60 16 62 163 64 z/. I < 28.12 27.30 27.41 28.41 28.41 27.08 27.22 27.28 28.22 28.48 27.70 2788 27.97 27.13 27.68 27.80 65 66 67 168 69 70 171 72 173 174 175 176 177 78 179 80 18 182 83 184 85 86 187 wherein the number in the column following the ion (n) is the nth ionization energy of the atom, for example, Pd + 32.93eV = Pd,3 " "+ + e and Li + e = Li + 5.39eV; (2) a two-ion couples capable of producing energy holes for shrinking hydrogen atoms involving cations and anions, selected from the group consisting of: 88 89 190 91 92 93 194 195 wherein the number in the column following the ion (n) is the nth ionization energy of the atom, for example, Ga + + 30.71eV = Ga 3+ + e " and H + e " = H " + 3.08eV; and (2) a cation and a molecule capable of producing energy holes for shrinking hydrogen atoms where the molecule is reduced, 196 97 198 wherein the number in the column following the ion or molecule (n) is the nth ionization energy of the atom or molecule, for example, Ga * + 30.71eV = Ga * + e and BF 3 + e BF 3 + 2.65eV. 199 3 3 . The apparatus of claim 18, wherein said means providing an energy hole is a substance comprising a plurality o elements of matter, each having an ionization energy, wherein each of said plurality of elements of matter are selected to produce a difference in ionization energies substantially equal to the resonance shrinkage energy of said first element of matter. 34. The apparatus of claim 33, wherein said energy hole is provided by one of the following three-ion couples: Atom (eV) Oxidized B 3 37.48. Cd 3 37.48 35. The apparatus of claim 18, further including: a pressurized gas energy reactor comprising at least a first vessel containing a source of hydrogen; a means to control the pressure of the vessel; a means to dissociate the molecular hydrogen into atomic hydrogen; a molten, liquid, or solid solution of the energy holes; a photon source, a second vessel; a power supply providing a current; a means to control said current, an external energy source, a heating means; computerized monitoring and control system; and a means that removes tne lower-energy hydrogen such as a selective venting valve to prevent the exothermic shrinkage reaction from coming to equilibrium 36. The apparatus of claim 35, wherein: tne inn r surface of the first vessel comoπses one or more of a coat of n'c el. platinum, o- palladium, and the outer surface of the f i rst vessel is coated with one or more cf copper, tellurium, arserlc, ces ium, olatinum, or pa!1aσ-um and 3n oxide such as Cu0χ , PtO χ , P d O χ, 37. The apparatus of claim 35, wherein: 'Xe lop.er surface of the first vessel 1s coatee ith one or mere of copoer, tel lurium, a r senic, cesium, platinum, or pai iadlum and an oxiαe s ch as Cu0χ PtO*. PdOχ, n0 x A10χ, 5 0χ . 200 38. The apparatus of claim 35 , wherein the source of energy holes is potassium carbonate . 39. The apparatus of claim 18 , further including : a gas discharge energy reactor comprising at least a hydrogen gas filleα glow discharge vacuum chamber; a hydrogen source, a control valve to control the flow of hydrogen from the hydrogen source to the gas discharge chamber, a molten, liquid, or solid solution of the energy hol es, a photon source; a cathode, an anode, a power supply providing a current; a means to control said current; an external energy source, a heating means, computerized monitoring and control system; and a means that removes the lower-energy hydrogen such as a selective venting valve to prevent the exothermic shrinkage reaction from coming to equilibrium. 40. The apparatus of claim 39 , wherein the cathode is palladium and the energy hole is provided by the transfer of two electrons from palladium to the discharge current. 41. Apparatus for providing the absorption of energy, comprising: means for providing an element of matter in a selected volume, said element having a nucleus and at least one electron comprising an orbital in a lower energy level than the "ground state" having a resonance shrinkage energy, and a means introduced into said selected volume for providing an energy hole in juxtaposi tion with said element of matter, said energy hole having a magnitude substantially equal to said resonance shrinkage energy, wherein energy is released to sai d element of matter when the orbital of said element of mattei is increased due to absorption of orbital, energy by said energy hole permitt ing the electron of the element of matter to be st imulated to undergo the reverse of at least one shrinkage transi t ion provi ding the absorption of energy 201 42 . The apparatus of claim 41 , further including : an electrolytic energy reactor, a pressurired gas energy reactor, and a gas discharge energy reactor, comprising a source of lower-energy hydrogen; a source of energy holes, a h source, and a means to remove the normal hydrogen such as a select iv venting valves to prevent the endothermic r : _ -.ion from coming to equil ibrium.

Inventors: MILLS RANDELL L, MILLS, RANDELL, L.
Applicants: HYDROCATALYSIS POWER CORP, HYDROCATALYSIS POWER CORPORATION
Application year: 1994
Main classification: G21B1
IPC codes: C01B3, F02G1, G21B1, G21B3